Question

QUESTION 4.

If
you have 2 randomly selected vectors like R and R;
Show that R. RX 5) = 0
(102)​

Answer 1

Follows are the solution to this question:

Step-by-step 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} * \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} * \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.