Explanation

(d)
Let ${\overrightarrow{\mathbf{R}}}_{1} = 2\widehat{\mathbf{i}} + 4\widehat{\mathbf{j}} - 5\widehat{\mathbf{k}}$
and ${\overrightarrow{\mathbf{R}}}_{2} = \widehat{\mathbf{i}} + 2\widehat{\mathbf{j}} + 3\widehat{\mathbf{k}}$
[image:10_image4.emf]
$\therefore\ \overrightarrow{\mathbf{R}}\ (along\ \overrightarrow{\mathbf{AC}}) = {\overrightarrow{\mathbf{R}}}_{1} + {\overrightarrow{\mathbf{R}}}_{2} = 3\widehat{\mathbf{i}} + 6\widehat{\mathbf{j}} - 2\widehat{\mathbf{k}}$
$\therefore\ \overrightarrow{\mathbf{a}}\ \left( unit\ vector\ angle\ \overrightarrow{AC}\ \right) = \frac{\overrightarrow{\mathbf{R}}}{|\overrightarrow{\mathbf{R}}|} = \frac{3\widehat{\mathbf{i}} + 6\widehat{\mathbf{j}} - 2\widehat{\mathbf{k}}}{\sqrt{9 + 36 + 4}}$
$= \frac{1}{7}\left( \ 3\widehat{\mathbf{i}} + 6\widehat{\mathbf{j}} - 2\widehat{\mathbf{k}}\ \right)$