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
BETA
