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 $



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