Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Hint: Let the angle be $\theta$. Then, $\cos \left(90^{\circ }-\theta \right)=\frac{(3\hat{\mathbf{i}}+4\hat{\mathrm{j}}+5\hat{\mathrm{k}})\cdot (2\hat{\mathrm{i}}-2\hat{\mathrm{j}}+\hat{\mathrm{k}})}{|3\hat{\mathrm{i}}+4\hat{\mathrm{j}}+5\hat{\mathrm{k}}|\times |2\hat{\mathbf{i}}-2\hat{\mathrm{j}}+\hat{\mathrm{k}}|}\Rightarrow \sin \theta =\frac{3}{\sqrt{50}\sqrt{9}}=\frac{\sqrt{2}}{10}$