Kinematics Question 36
Question: The vector sum of two forces is perpendicular to their vector differences. In that case, the forces [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:
If two vectors are perpendicular then their dot product must be equal to zero. According to problem $ (\overrightarrow{A}+\overrightarrow{B}).(\overrightarrow{A}-\overrightarrow{B})=0 $
therefore $ \overrightarrow{A}.\overrightarrow{A}-\overrightarrow{A}.\overrightarrow{B}+\overrightarrow{B}.\overrightarrow{A}-\overrightarrow{B}.\overrightarrow{B}=0 $
therefore $ A^{2}-B^{2}=0 $
therefore $ A^{2}=B^{2} $
$ \therefore $ $ A=B $ i.e. two vectors are equal to each other in magnitude.
BETA
