Mathematics - Vector Question with Solution | TestHub

$$\begin{array}{rl}& \ell =\cos 45^{\circ }=\frac{1}{\sqrt{2}}\\ & m=\cos 120^{\circ }=-\frac{1}{2}\\ & n=\cos \theta \end{array}$$ where $\theta$ is the angle which line makes with positive z-axis. Now ${\ell }^2+m^2+n^2=1$ \begin{aligned} & \Rightarrow \frac{1}{2}+\frac{1}{4}+\cos ^2 \theta=1 \\ & \cos ^2 \theta=\frac{1}{4} \\ & \Rightarrow \cos \theta=\frac{1}{2} ( $\theta$ Being acute)\\ & \Rightarrow \theta=\frac{\pi}{3} \end{aligned}