CUET Preparation Today
The direction cosines of a vector equally inclined to the axes \(OX,OY\) and \(OZ\) are |
\(\frac{1}{2},\frac{1}{2},\frac{1}{2}\) \(\frac{1}{3},\frac{1}{3},\frac{1}{3}\) \(\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}\) \(0,0,1\) |
\(\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}\) |
| \(\begin{aligned}l=\cos \alpha, m=\cos \alpha, n&=\cos \alpha\\ l^{2}+m^{2}+n^{2}&=1\\ 3\cos^{2} \alpha &=1\\ \cos^{2}\alpha &=\frac{1}{3}\\ \cos \alpha &=\frac{1}{\sqrt{3}}\end{aligned}\) |
