Question

Vector $\overrightarrow{A}$ makes equal angles with $x-,y-$, and $z$-axes. Find the value of its components (in terms of magnitude of $\overrightarrow{A}$)

Answer 1

Let vector $\overrightarrow{A}$ makes angle $\alpha ,\beta ,\gamma$ with $x,y$ & $z$ respectively. Then we know that.

${\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma =1$

it is given that $\alpha =\beta =\gamma$

So, ${3\cos }^2\alpha =3{\cos }^2\beta =3{\cos }^2\gamma =1$

$\cos \alpha =\frac{1}{\sqrt{3}}=\cos \beta =\cos \gamma$

So, $\overrightarrow{A}=\frac{1}{\sqrt{3}}\hat{i}+\frac{1}{\sqrt{3}}\hat{j}+\frac{1}{\sqrt{3}}\hat{k}$