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.



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