Assertion And Reason MCQs On Motion In A Plane (Vectors) For Class 11 Physics, JEE, NEET

Prepare effectively for Assertion and Reason Questions with Answers and Explanations on Motion in a Plane (Vectors) for Class 11 Physics CBSE Board Exam with carefully selected conceptual questions and detailed explanations. These assertion and reason MCQs are designed according to the latest CBSE syllabus and are also useful for CBSE Board Exam, JEE Main, NEET, and other competitive exams. Practising these questions will strengthen your understanding of vectors, vector addition, resolution of vectors, scalar and vector quantities, and motion in a plane while improving your logical reasoning and analytical skills.

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Assertion and Reason MCQs of Chapter Motion in a Plane (Vectors) for Class 11 Physics CBSE Board, JEE and NEET Exams with Answers and Explanations
Answers and Explanations of Assertion and Reason MCQs on Motion in a Plane (Vectors) for Class 11 Physics CBSE Board, JEE and NEET Exams

Assertion and Reason MCQs of Chapter Motion in a Plane (Vectors) for Class 11 Physics CBSE Board, JEE and NEET Exams with Answers and Explanations

Read the assertion and reason carefully to mark the correct option out of the options given below:
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

Assertion: $\vec{A} \times \vec{B}$ is perpendicular to both $\vec{A} + \vec{B}$ as well as $\vec{A} - \vec{B}$ .

Reason: $\vec{A} + \vec{B}$ as well as $\vec{A} - \vec{B}$ lie in the plane containing $\vec{A}$ and $\vec{B}$ , but $\vec{A} \times \vec{B}$ lies perpendicular to the plane containing $\vec{A}$ and $\vec{B}$ .

Understand related topics like Motion in a Plane (Vectors) MCQs for Class 11 Physics With Answers and Solutions

Assertion: Angle between $\hat{i} + \hat{j}$ and $\hat{i}$ is $45^{\circ}$ .

Reason: $\hat{i} + \hat{j}$ is equally inclined to both $\hat{i}$ and $\hat{j}$ and the angle between $\hat{i}$ and $\hat{j}$ is $90^{\circ}$ .

Enhance your preparation with NCERT Solutions for Vectors Class 11 Physics Chapter Motion in a Plane

Assertion: If $θ$ be the angle between $\vec{A}$ and $\vec{B}$ , then $\tan θ = \frac{| \vec{A} \times \vec{B} |}{\vec{A} \cdot \vec{B}}$ .

Reason: $\vec{A} \times \vec{B}$ is perpendicular to $\vec{A} \cdot \vec{B}$ .

Practice more questions from NCERT Exemplar Solutions for Vectors Class 11 Physics Motion in a Plane

Assertion: If $| \vec{A} + \vec{B} | = | \vec{A} - \vec{B} |$ , then angle between $\vec{A}$ and $\vec{B}$ is $90^{\circ}$ .

Reason: $\vec{A} + \vec{B} = \vec{B} + \vec{A}$ .

Assertion: Vector product of two vectors is an axial vector.

Reason: If $\vec{v}$ = instantaneous velocity, $\vec{r}$ = radius vector and $\vec{ω}$ = angular velocity, then $\vec{v} = \vec{ω} \times \vec{r}$ .

Assertion: Minimum number of non-equal vectors in a plane required to give zero resultant is three.

Reason: If $\vec{A} + \vec{B} + \vec{C} = \vec{0}$ , then they must lie in one plane.

Assertion: Relative velocity of A w.r.t. B is greater than the velocity of either, when they are moving in opposite directions.

Reason: Relative velocity of A w.r.t. B is ${\vec{v}}_{A B} = {\vec{v}}_{A} - {\vec{v}}_{B}$ .

Assertion: Vector addition of two vectors $\vec{A}$ and $\vec{B}$ is commutative.

Reason: $\vec{A} + \vec{B} = \vec{B} + \vec{A}$ .

Assertion: $\vec{A} \cdot \vec{B} = \vec{B} \cdot \vec{A}$ .

Reason: Dot product of two vectors is commutative.

10.

Assertion: $\vec{τ} = \vec{r} \times \vec{F}$ and $\vec{τ} \neq \vec{F} \times \vec{r}$ .

Reason: Cross product of vectors is commutative.

11.

Assertion: A negative acceleration of a body is associated with a slowing down of a body.

Reason: Acceleration is a vector quantity.

12.

Assertion: A physical quantity cannot be called as a vector if its magnitude is zero.

Reason: A vector has both, magnitude and direction.

13.

Assertion: The sum of two vectors can be zero.

Reason: The vectors cancel each other, when they are equal and opposite.

14.

Assertion: Two vectors are said to be like vectors if they have same direction but different magnitude.

Reason: Vector quantities do not have specific direction.

15.

Assertion: The scalar product of two vectors can be zero.

Reason: If two vectors are perpendicular to each other, their scalar product will be zero.

16.

Assertion: Multiplying any vector by a scalar is a meaningful operation.

Reason: In uniform motion speed remains constant.

17.

Assertion: A null vector is a vector whose magnitude is zero and direction is arbitrary.

Reason: A null vector does not exist.

18.

Assertion: If dot product and cross product of $\vec{A}$ and $\vec{B}$ are zero, it implies that one of the vectors $\vec{A}$ and $\vec{B}$ must be a null vector.

Reason: Null vector is a vector with zero magnitude.

19.

Assertion: The cross product of a vector with itself is a null vector.

Reason: The cross-product of two vectors results in a vector quantity.

20.

Assertion: The minimum number of non-coplanar vectors whose sum can be zero, is four.

Reason: The resultant of two vectors of unequal magnitude can be zero.

Assertion: If $\vec{A} \cdot \vec{B} = \vec{B} \cdot \vec{C}$ , then $\vec{A}$ may not always be equal to $\vec{C}$ .

Reason: The dot product of two vectors involves cosine of the angle between the two vectors.

22.

Assertion: Vector addition is commutative.

Reason: $(\vec{A} + \vec{B}) \neq (\vec{B} + \vec{A})$ .

23.

Assertion : Magnitude of resultant of two vectors may be less than the magnitude of either vector.

Reason: Vector addition is commutative.

Assertion: Vector addition of two vectors is always greater than their vector subtraction.

Reason: At θ = 90°, addition and subtraction of vectors are equal

Answers and Explanations of Assertion and Reason MCQs on Motion in a Plane (Vectors) for Class 11 Physics CBSE Board, JEE and NEET Exams

1. Answer: (a)

Assertion is True: The cross product $\vec{A} \times \vec{B}$ is perpendicular to the plane containing both $\vec{A}$ and $\vec{B}$ . Since both $(\vec{A} + \vec{B})$ and $(\vec{A} - \vec{B})$ lie entirely within that same plane, $\vec{A} \times \vec{B}$ is perpendicular to both of them.
Reason is True & Correct Explanation: The reason accurately explains why the perpendicularity holds based on coplanar geometry.

2. Answer: (a)

Assertion is True: The angle $θ$ between $\hat{i} + \hat{j}$ and $\hat{i}$ can be found using the dot product: $\cos θ = \frac{(\hat{i} + \hat{j}) \cdot \hat{i}}{| \hat{i} + \hat{j} | | \hat{i} |} = \frac{1}{\sqrt{2}}$ , which gives $θ = 45^{\circ}$ .
Reason is True & Correct Explanation: Because $\hat{i}$ and $\hat{j}$ are mutually perpendicular ( $90^{\circ}$ ) and have equal magnitudes, their resultant vector ( $\hat{i} + \hat{j}$ ) bisects the angle perfectly, making it $45^{\circ}$ to both axes.

3. Answer: (b)

Assertion is True: $| \vec{A} \times \vec{B} | = A B \sin θ$ and $\vec{A} \cdot \vec{B} = A B \cos θ$ . Therefore, $\frac{| \vec{A} \times \vec{B} |}{\vec{A} \cdot \vec{B}} = \frac{A B \sin θ}{A B \cos θ} = \tan θ$ . (Assuming standard magnitudes are implied).
Reason is True: The cross product $\vec{A} \times \vec{B}$ is indeed always perpendicular to the dot product scalar plane (or directly perpendicular to individual component vectors), but this fact is not the mathematical derivation or explanation for why the ratio equals $\tan θ$ .

4. Answer: (b)

Assertion is True: Squaring both sides of $| \vec{A} + \vec{B} | = | \vec{A} - \vec{B} |$ gives $A^{2} + B^{2} + 2 A B \cos θ = A^{2} + B^{2} - 2 A B \cos θ$ . This simplifies to $4 A B \cos θ = 0 ⟹ \cos θ = 0 ⟹ θ = 90^{\circ}$ .
Reason is True: Vector addition is commutative ( $\vec{A} + \vec{B} = \vec{B} + \vec{A}$ ), but this property has nothing to do with finding the angle between the vectors.

5. Answer: (c) / (d) depending on notation standard

Assertion is True: Vector products (like torque, angular velocity) are axial vectors because they point along the axis of rotation.
Reason is False: The correct formula relating linear velocity, angular velocity, and radius vector is $\vec{v} = \vec{ω} \times \vec{r}$ . The reason states $\vec{v} = \vec{r} \times \vec{ω}$ , which is incorrect due to the directional nature of cross products ( $\vec{r} \times \vec{ω} = - \vec{v}$ ).

6. Answer: (b)

Assertion is True: To get a zero resultant with non-equal vectors in a single plane, you need a minimum of 3 vectors forming a closed triangle.
Reason is True: If $\vec{A} + \vec{B} + \vec{C} = 0$ , then $\vec{A} + \vec{B} = - \vec{C}$ , which forces all three vectors to lie in the same plane. However, the reason does not explicitly explain why the vectors must be non-equal to set the minimum limit to three.

7. Answer: (b)

Assertion is True: When moving in opposite directions, relative velocity magnitude is $v_{A} - (- v_{B}) = v_{A} + v_{B}$ , which is greater than either individual velocity.
Reason is True: The general vector formula for relative velocity is ${\vec{v}}_{A B} = {\vec{v}}_{A} - {\vec{v}}_{B}$ . However, this mathematical formula alone does not intuitively explain the physical condition of moving in opposite directions causing a magnitude increase.

8. Answer: (a)

Assertion is True: Vector addition strictly follows the commutative law.
Reason is True & Correct Explanation: The statement $\vec{A} + \vec{B} = \vec{B} + \vec{A}$ is the literal definition of the commutative property.

9. Answer: (a)

Assertion is True: $\vec{A} \cdot \vec{B} = \vec{B} \cdot \vec{A}$ .
Reason is True & Correct Explanation: The reason states the structural property that justifies the assertion.

10. Answer: (c)

Assertion is True: Torque is defined as $\vec{τ} = \vec{r} \times \vec{F}$ . Since cross products are anti-commutative ( $\vec{r} \times \vec{F} = - (\vec{F} \times \vec{r})$ ), $\vec{τ} \neq \vec{F} \times \vec{r}$ .
Reason is False: Cross product of vectors is anti-commutative, not commutative.

11. Answer: (e)

Assertion is False: Negative acceleration (retardation) only slows a body down if it opposes the direction of velocity. If velocity is already negative, a negative acceleration actually causes the object to speed up.
Reason is True: Acceleration is a vector quantity.

12. Answer: (e)

Assertion is False: A vector with zero magnitude is defined perfectly in physics as a null vector or zero vector ( $\vec{0}$ ).
Reason is True: By definition, a vector possesses both magnitude and direction.

13. Answer: (a)

Assertion is True: The vector sum can absolutely equal zero.
Reason is True & Correct Explanation: When two vectors are equal in magnitude and point in exactly opposite directions ( $180^{\circ}$ ), they cancel completely.

14. Answer: (c)

Assertion is True: “Like vectors” (or parallel vectors) point in the exact same direction but can have entirely different lengths/magnitudes.
Reason is False: Vector quantities always possess specific, definitive directions.

15. Answer: (a)

Assertion is True: The scalar (dot) product can equal zero.
Reason is True & Correct Explanation: For perpendicular vectors, $θ = 90^{\circ}$ , making $\vec{A} \cdot \vec{B} = A B \cos (90^{\circ}) = 0$ .

16. Answer: (b)

Assertion is True: Scaling a vector changes its magnitude (and completely reverses its direction if scaled by a negative number), which is a physically meaningful operation.
Reason is True: In uniform motion, speed is constant. However, this statement has no logical correlation to scaling random vectors.

17. Answer: (c)

Assertion is True: A null vector has zero magnitude and its direction cannot be uniquely determined (arbitrary).
Reason is False: Null vectors exist and are physically meaningful (e.g., the position vector of the origin, or velocity of a stationary object).

18. Answer: (b)

Assertion is True: If $\vec{A} \cdot \vec{B} = 0$ , they are perpendicular ( $θ = 90^{\circ}$ ). If $\vec{A} \times \vec{B} = 0$ , they are parallel ( $θ = 0^{\circ}$ or $180^{\circ}$ ). Because a pair of nonzero vectors cannot be both parallel and perpendicular at the same time, at least one of them must be a null vector.
Reason is True: A null vector does have zero magnitude, but this definition on its own doesn’t completely explain the simultaneous conditions of both products being zero.

19. Answer: (b)

Assertion is True: The cross product of a vector with itself is $\vec{A} \times \vec{A} = A^{2} \sin (0^{\circ}) \hat{n} = \vec{0}$ (null vector).
Reason is True: The cross product yields a vector quantity, but it doesn’t explain why the specific angle of $0^{\circ}$ yields zero.

20. Answer: (c)

Assertion is True: Three non-coplanar vectors can never yield a closed loop to cancel out to zero; you need a minimum of 4 non-coplanar vectors to get a net resultant of zero.
Reason is False: The resultant of two vectors of unequal magnitude can never be zero because they cannot perfectly cancel each other out.

21. Answer: (a)

Assertion is True: If $\vec{A} \cdot \vec{B} = \vec{B} \cdot \vec{C}$ , it simplifies to $\vec{B} \cdot (\vec{A} - \vec{C}) = 0$ . This means either $\vec{A} = \vec{C}$ , OR the vector $(\vec{A} - \vec{C})$ is perpendicular to $\vec{B}$ . Hence, $\vec{A}$ does not always have to equal $\vec{C}$ .
Reason is True & Correct Explanation: The presence of the cosine term ( $\cos θ$ ) allows different vector orientations to yield identical dot product scalar values.

22. Answer: (c)

Assertion is True: Vector addition is commutative ( $\vec{A} + \vec{B} = \vec{B} + \vec{A}$ ).
Reason is False: The statement mathematically claims equality with an inverted negative vector order $(\vec{A} - \vec{B}) \neq (\vec{B} - \vec{A})$ or incorrectly frames structural notation.

23. Answer: (b)

Assertion is correct: The magnitude of the resultant $| \vec{A} + \vec{B} |$ depends on the angle between them. For example, if two vectors of magnitude 5 units are opposite to each other ( $180^{\circ}$ ), their resultant magnitude is $5 - 5 = 0$ , which is less than the magnitude of either vector.

Reason is correct: Vector addition is indeed commutative ( $\vec{A} + \vec{B} = \vec{B} + \vec{A}$ ). However, this algebraic property does not explain why or how the magnitude changes with the orientation angle.

24. Answer: (e)

Assertion is incorrect: The magnitude of vector addition $| \vec{A} + \vec{B} |$ is not always greater than vector subtraction $| \vec{A} - \vec{B} |$ . If the angle $θ$ between the vectors is obtuse (90° < θ < 180°), the magnitude of their subtraction is actually greater than their addition.

Reason is correct: At $θ = 90^{\circ}$ , we have $\cos 90^{\circ} = 0$ . Both formulas yield the same value: $| \vec{A} + \vec{B} | = \sqrt{A^{2} + B^{2}}$ and $| \vec{A} - \vec{B} | = \sqrt{A^{2} + B^{2}}$ .