Question

QUESTION 4.

Answer 1

Answer:

Follows are the solution to this question:

Explanation:

Please find the correct question in the attachment file.

Let:

$\overrightarrow{R}= R_i\hat{i}+R_j\hat{j}+R_k\hat{k}\\\\\overrightarrow{S}= S_i\hat{i}+S_j\hat{j}+S_k\hat{k}$

Calculating the value of  $\overrightarrow{R} \times \overrightarrow{S}:$

$\to \left | \begin{array}{ccc}\hat{i}&\hat{j}&\hat{K}\\R_i&R_j&R_k\\S_i&S_j&S_k\end{array}\right | = \hat{i}[R_j S_k-S_jR_k]-\hat{j}[R_i S_k-S_iR_k]+\hat{k}[R_i S_j-S_iR_j]$

Calculating the value of $\overrightarrow{R} \cdot (\overrightarrow{R} \times \overrightarrow{S}):$

$\to (R_i\hat{i}+R_j\hat{j}+R_k\hat{k}) \cdot ( \hat{i}[R_j S_k-S_jR_k]-\hat{j}[R_i S_k-S_iR_k]+\hat{k}[R_i S_j-S_iR_j])$

by solving this value it is equal to 0.