Laws Of Motion Question 69
Question: The vector sum of two forces is perpendicular to their vector differences. In that case, the force [CBSE PMT 2003]
Options:
A) Are equal to each other in magnitude
B) Are not equal to each other in magnitude
C) Cannot be predicted
D) Are equal to each other
Show Answer
Answer:
Correct Answer: A
Solution:
Let two vectors be $ \overrightarrow{A} $ and $ \overrightarrow{B} $ then $ (\overrightarrow{A}+\overrightarrow{B}).(\overrightarrow{A}-\overrightarrow{B})=0 $
$ \overrightarrow{A}\ .\ \overrightarrow{A}-\overrightarrow{B}\ .\ \overrightarrow{B}+\overrightarrow{B}\ .\ \overrightarrow{A}-\overrightarrow{B}\ .\ \overrightarrow{B}=0 $
$ A^{2}-B^{2}=0 $ therefore$ A^{2}=B^{2} $
$ \therefore \ \ A=B $
