Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

We have $|\overline{\mathrm{u}}|=2$ and $\cos \alpha =60^{\circ }=\frac{1}{2}$ and $\cos \beta =\cos 120^{\circ }=-\frac{1}{2}$ Now ${\cos }^2\gamma =1-\left(\frac{1}{4}+\frac{1}{4}\right)=\frac{1}{2}\Rightarrow \cos \gamma =\pm \frac{1}{\sqrt{2}}$ Thus direction of $\overline{\mathrm{u}}$ are $1,-1,\pm \sqrt{2}$ $\therefore \overline{\mathrm{u}}=2(\hat{\mathrm{i}}-\hat{\mathrm{j}}\pm \sqrt{2}\hat{\mathrm{k}})$