Vectors A→ and B→ are mutually perpendicular. Component of A→ + B→ in the direction of A→ - B→ will be :

A
$\frac{A^{2} + B^{2}}{\sqrt{A^{2} - B^{2}}}$
B
$\sqrt{A^{2} - B^{2}}$
C
$\frac{A + B}{A - B}$
D
$\frac{A^{2} - B^{2}}{\sqrt{A^{2} + B^{2}}}$

Solution:

Component of $\vec{A}$ + $\vec{B}$ in the direction of $\vec{A} - \vec{B} = (\vec{A} + \vec{B}) . (\frac{\vec{A} - \vec{B}}{|\vec{A} - \vec{B}|}) = \frac{A^{2} - B^{2}}{\sqrt{A^{2} + B^{2}}}$

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