Mathematics - Vector Question with Solution | TestHub

We know that, projection of $\mathbf{a}$ on $\mathbf{b}$ is given by projection, $|\mathrm{a}|\cos \theta =\frac{(\mathbf{a}\cdot \mathbf{b})}{|\mathbf{b}|}$ Let line joining points $(3,4,5)$ and $(4,6,3)$ is $L_1$ and line joining points $(-1,2,4)$ and $(1,0,5)$ is $L_2$ $\Rightarrow \begin{array}{rl}& L_1=\hat{\mathbf{i}}+2\hat{\mathbf{j}}-2\hat{\mathbf{k}}\\ & L_2=2\hat{\mathbf{i}}-2\hat{\mathbf{j}}+\hat{\mathbf{k}}\end{array}$ $\therefore$ Projection of $L_1$ and $L_2=\frac{L_1\cdot L_2}{|L_2|}$ $=\frac{2-4-2}{\sqrt{4+4+1}}=\frac{-4}{3}$ $\therefore$ Magnitude $=\frac{4}{3}$