Mathematics - Vector Question with Solution | TestHub

The shortest distance between $L_1$ and $L_2$ is $$\begin{array}{r}\left|\frac{\{(2-(-1))\hat{\mathbf{i}}+(2-2)\hat{\mathbf{j}}+(3-(-1))\hat{\mathbf{k}}\}\cdot (-\hat{\mathbf{i}}-7\hat{\mathbf{j}}+5\hat{\mathbf{k}})}{5\sqrt{3}}\right|\\ =\left|\frac{(3\hat{\mathbf{i}}+4\hat{\mathbf{k}})\cdot (-\hat{\mathbf{i}}-7\hat{\mathbf{j}}+5\hat{\mathbf{k}})}{5\sqrt{3}}\right|=\frac{17}{5\sqrt{3}}\end{array}$$