Assertion $\left(\mathrm{A}\right):$ If $\overline{a}, \overline{b}$ are two non-collinear vectors then the vector component of $\overline{b}$ along the line perpendicular to $\overline{a}$ is $\frac{\overline{a}\times (\overline{b}\times \overline{a})}{|\overline{a}{|}^2}$.
Reason $\left(\mathrm{R}\right): \overline{a}\times (\overline{b}\times \overline{c})=(\overline{a}·\overline{c})\overline{b}-(\overline{a}·\overline{b})\overline{c}$ and vector component of $\overline{b}$ on $\overline{c}$ is $\left(\overline{b}·\frac{\overline{c}}{\left|\overline{c}\right|}\right)\frac{\overline{c}}{\left|\overline{c}\right|}$.

• Correct answer
  A

  Both $\left(\mathrm{A}\right)$ and $\left(\mathrm{R}\right)$ are true and $\left(\mathrm{R}\right)$ is the correct explanation of $\left(\mathrm{A}\right)$
• B

  Both $\left(\mathrm{A}\right)$ and $\left(\mathrm{R}\right)$ are true but $\left(\mathrm{R}\right)$ is not the correct explanation of $\left(\mathrm{A}\right)$
• C

  $\left(\mathrm{A}\right)$ is true but $\left(\mathrm{R}\right)$ is false
• D

  $\left(\mathrm{A}\right)$ is false but $\left(\mathrm{R}\right)$ is true

Hence, the correct answer is option: 'A'.