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Q.
If for two vector $\vec{A}$ and $\vec{B}$, sum $(\vec{A}+\vec{B})$ is perpendicular to the difference $(\vec{A}-\vec{B})$. The ratio of their magnitude is
Motion in a Plane
Solution:
Sol. (a) $(\vec{A}+\vec{B})$ is perpendicular to $(\vec{A}-\vec{B})$.
Thus$(\vec{A}+\vec{B}) \cdot(\vec{A}-\vec{B})=0$
or $A^{2}+\vec{B} \cdot \vec{A}-\vec{A} \cdot \vec{B}-B^{2}=0$
Because of commutative property of dot product $\vec{A} \cdot \vec{B}=\vec{B} \cdot \vec{A}$
$\therefore A^{2}-B^{2}=0$ or $A=B$
Thus the ratio of magnitudes $A / B=1$