The vector component $\overrightarrow{\mathit{b}}$ along the line parallel to $\overrightarrow{\mathit{a}}$ is

$\left(\frac{\overrightarrow{a}·\overrightarrow{b}}{\left|\overrightarrow{a}\right|}\right)\frac{\overrightarrow{a}}{\left|\overrightarrow{a}\right|}$

The figure below represents the vectors.

$\overline{OA}=\left(\frac{\overrightarrow{a}·\overrightarrow{b}}{\left|\overrightarrow{a}\right|}\right)\overrightarrow{a}$

Now,

$\overrightarrow{\mathit{A}\mathit{B}}\mathit{=}\overrightarrow{\mathit{O}\mathit{B}}\mathit{-}\overrightarrow{\mathit{O}\mathit{A}}$

$\mathit{=}\overrightarrow{b}\mathit{-}\left(\frac{\overrightarrow{a}\mathit{·}\overrightarrow{b}}{\left|{\overrightarrow{a}}^{\mathit{2}}\right|}\right)\overrightarrow{a}$

$\mathit{=}\frac{\mathit{(}\overrightarrow{\mathit{a}}\mathit{·}\overrightarrow{\mathit{a}}\mathit{)}\overrightarrow{\mathit{b}}\mathit{-}\mathit{(}\overrightarrow{\mathit{a}}\mathit{·}\overrightarrow{\mathit{b}}\mathit{)}\overrightarrow{\mathit{a}}}{\left|{\overrightarrow{\mathit{a}}}^{\mathit{2}}\right|}$

$\mathit{=}\frac{\overrightarrow{a}\mathit{\times }\mathit{(}\overrightarrow{b}\mathit{\times }\overrightarrow{a}\mathit{)}}{\left|{\overrightarrow{a}}^{\mathit{2}}\right|}$

Thus, (A) and (R) are true and (R) is the correct explanation.