Motion in A Plane - NEET Questions Physics

(4)

Let the two vectors be $\vec{A}$ and $\vec{B}$ .

Then, magnitude of sum of $\vec{A}$ and $\vec{B},$ $| \vec{A} + \vec{B} |$ $= \sqrt{A^{2} + B^{2} + 2 A B \cos θ}$

and magnitude of difference of $\vec{A}$ and $\vec{B}$

$| \vec{A} - \vec{B} |$ $= \sqrt{A^{2} + B^{2} - 2 A B \cos θ}, | \vec{A} + \vec{B} | = | \vec{A} - \vec{B} | (given)$

or $\sqrt{A^{2} + B^{2} + 2 A B \cos θ} = \sqrt{A^{2} + B^{2} - 2 A B \cos θ}$

$\Rightarrow 4 A B \cos θ = 0$ $∵$ $4 A B \neq 0,$ $∴$ $\cos θ = 0 or θ = 90 °$

Want Us to Email you About Special Offers & Updates?