Motion in a Plane - Result Question 2

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2. If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is : [2016]

======= ####2. If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is : [2016]

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/motion-in-a-plane/motion-in-a-plane—result-question-2.md (a) $0^{\circ}$

(b) $90^{\circ}$

(c) $45^{\circ}$

(d) $180^{\circ}$

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Answer:

Correct Answer: 2. (b)

Solution:

  1. (b) $|\overrightarrow{{}A}+\overrightarrow{{}B}|=|\overrightarrow{{}A}-\overrightarrow{{}B}|$

Squaring on both sides

$ \begin{aligned} & |\overrightarrow{{}A}+\overrightarrow{{}B}|^{2}=|\overrightarrow{{}A}-\overrightarrow{{}B}|^{2} \\ & \Rightarrow \overrightarrow{{}A} \cdot \overrightarrow{{}A}+2 \overrightarrow{{}A} \cdot \overrightarrow{{}B}+\overrightarrow{{}B} \cdot \overrightarrow{{}B} \\ & \quad=\overrightarrow{{}A} \cdot \overrightarrow{{}A}-2 \overrightarrow{{}A} \cdot \overrightarrow{{}B}+\overrightarrow{{}B} \cdot \overrightarrow{{}B} \\ & \Rightarrow 4 \overrightarrow{{}A} \cdot \overrightarrow{{}B}=0 \Rightarrow 4 AB \cos \theta=0 \\ & \Rightarrow \cos \theta=0 \Rightarrow \theta=90^{\circ} \end{aligned} $