Question

Write a vector of magnitude $3\sqrt{3}$ in the direction of vector joining the points $A(2,3,4)$ and $B(4,6,7)$.

Answer 1

$\begin{array}{c}A\left(2,3,4\right)B\left(4,6,7\right)\\ \overrightarrow{AB}=\left(2,3,3\right)\\ \widehat{AB}=\frac{2}{\sqrt{22}},\frac{3}{\sqrt{22}},\frac{3}{\sqrt{22}}\\ \overrightarrow{d}=3\sqrt{3}\left(\frac{2}{\sqrt{22}},\frac{3}{\sqrt{22}},\frac{3}{\sqrt{22}}\right)\\ =\left(\frac{6\sqrt{3}}{\sqrt{22}}\hat{i},\frac{9\sqrt{3}}{\sqrt{22}}\hat{j},\frac{9\sqrt{3}}{\sqrt{22}}\hat{k}\right)\end{array}$