SATHEE: Kinematics Question 44

Kinematics Question 44

Question: Assertion : If $| \vec{A} + \vec{B} | = | \vec{A} - \vec{B} |$ , then angle between $\vec{A}$ and $\vec{B}$ is 90° Reason : $\vec{A} + \vec{B} = \vec{B} + \vec{A}$

Options:

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.

Show Answer

Answer:

Correct Answer: B

Solution:

$| \vec{A} + \vec{B} | = | \vec{A} - \vec{B} |$

therefore $A^{2} + B^{2} + 2 A B \cos θ$

= $A^{2} + B^{2} + 2 A B \cos θ$

Hence $\cos θ = 0$ which gives $θ = 90^{\circ}$ Also vector addition is commutative.

Hence $\vec{A} + \vec{B} = \vec{B} + \vec{A} .$

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Kinematics Question 44

Question: Assertion : If |A→+B→| = |A→−B→| , then angle between A→ and B→ is 90° Reason : A→+B→ = B→+A→

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Question: Assertion : If $| \vec{A} + \vec{B} | = | \vec{A} - \vec{B} |$ , then angle between $\vec{A}$ and $\vec{B}$ is 90° Reason : $\vec{A} + \vec{B} = \vec{B} + \vec{A}$