A) are not equal to each other in magnitude
B) cannot be predicted
C) are equal to each other
D) are equal to each other in magnitude
Correct Answer: D
Solution :
Key Idea: The two vectors must be perpendicular if their dot product must be zero. Let \[\vec{A}\] and \[\vec{B}\] are two forces. The sum of the two forces. \[{{\vec{F}}_{1}}=\vec{A}+\vec{B}.....(i)\] The difference of the two forces, \[{{\vec{F}}_{2}}=\vec{A}-\vec{B}.....(ii)\] Since, sum of the two forces is perpendicular to their differences as given, so \[{{\vec{F}}_{1}}\,.\,{{\vec{F}}_{2}}=0\] \[or(\vec{A}+\vec{B})\,.\,(\vec{A}-\vec{B})=0\] \[or{{A}^{2}}-\vec{A}\,.\,\vec{B}\,+\vec{B}\,.\,\vec{A}-{{B}^{2}}=0\] \[or{{A}^{2}}={{B}^{2}}\] \[or|\vec{A}|\,=\,|\vec{B}|\] Thus, the forces are equal to each other in magnitude.
You need to login to perform this action.
You will be redirected in
3 sec
