Question

Two vectors $A$ and $\sqrt{3}A$ are acting perpendicular to each other. What is the angle of resultant vector with $A$

Answer 1

We know resultant of vectors is given by

$A=\sqrt{A^2+{\left(\sqrt{3A}\right)}^2+2\left(A\sqrt{3A}\right)\cos \theta }$

$A^2=4A^2+2\sqrt{3}{A}^2\cos \theta$

$\cos \theta =\frac{-\sqrt{3}}{2}$

$\theta ={\cos }^{-1}\frac{\sqrt{3}}{2}$

$\theta ={150}^0$