Kinematics Question 256

Question: If for two vector $ \overrightarrow{A} $ and $ \overrightarrow{B} $ , sum $ (\overrightarrow{A}+\overrightarrow{B}) $ is perpendicular to the difference $ (\overrightarrow{A}-\overrightarrow{B}) $ . The ratio of their magnitude it’s

Options:

A) 1

B) 2

C) 3

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

$ (\overrightarrow{A}+\overrightarrow{B}) $ is perpendicular to $ (\overrightarrow{A}-\overrightarrow{B}) $ . Thus

$ (\overrightarrow{A}+\overrightarrow{B}) $ . $ (\overrightarrow{A}-\overrightarrow{B}) $ = 0

or $ A^{2}+\overrightarrow{B}.\overrightarrow{A}-\overrightarrow{A}.\overrightarrow{B}-B^{2}=0 $

Because of commutative property of dot product $ \overrightarrow{A}.\overrightarrow{B}=\overrightarrow{B}.\overrightarrow{A} $
$ \therefore $ $ A^{2}-B^{2}=0 $ or $ A=B $

Thus the ratio of magnitudes A/B = 1



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