MCQ
The vector sum of two forces is perpendicular to their vector differences. In that case, the forces
- ✓Are equal to each other in magnitude
- BAre not equal to each other in magnitude
- CCannot be predicted
- DAre equal to each other
✓
Answer
Correct option: A.
Are equal to each other in magnitude
(a) If two vectors are perpendicular then their dot product must be equal to zero. According to problem$\begin{aligned}& (\vec{A}\vec{B}) \cdot(\vec{A}-\vec{B})=0 \Rightarrow \vec{A} \cdot \vec{A}-\vec{A} \cdot \vec{B}+\vec{B} \cdot \vec{A}-\vec{B} \cdot \vec{B}=0 \\& \Rightarrow A^2-B^2=0 \Rightarrow A^2=B^2\end{aligned}$$\therefore A=B$ i.e. two vectors are equal to each other in magnitude.
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