MCQ
If for two vector $\vec{A}$ and $\vec{B}$, sum $(\vec{A} \quad \vec{B})$ is perpendicular to the difference $\left(\begin{array}{ll}A & \vec{B}\end{array}\right)$. The ratio of their magnitude is
- ✓1
- B2
- C3
- DNone of these
✓
Answer
Correct option: A.
1
(a) $(\vec{A}+\vec{B})$ is perpendicular to $(\vec{A}-\vec{B})$. Thus$\begin{aligned}& (\vec{A}+\vec{B}) \cdot(\vec{A}-\vec{B})=0 \\& \text { or } A^2+\vec{B} \cdot \vec{A}-\vec{A} \cdot \vec{B}-B^2=0\end{aligned}$Because of commutative property of dot product $\vec{A} \cdot \vec{B}=\vec{B} \cdot \vec{A}$$\therefore A^2-B^2=0 \text { or } A=B$Thus the ratio of magnitudes $A / B=1$
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