Question

Pleaseeeee pleaseeee helppppppppp​

Answer 1

Given:

The two vectors are:

`\overrightarrow{a}=2\hat{i}-\hat{j}+\hat{k}`

`\overrightarrow{b}=\hat{i}-3\hat{j}+5\hat{k}`

To find:

The value of
`|\overrightarrow{a}* \overrightarrow{b}|`.

Solution:

We have,

`\overrightarrow{a}=2\hat{i}-\hat{j}+\hat{k}`

`\overrightarrow{b}=\hat{i}-3\hat{j}+5\hat{k}`

The cross product of these two vectors is:

`\overrightarrow{a}* \overrightarrow{b}=\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\\2&-1&1\\1&-3&5\end{vmatrix}`

`\overrightarrow{a}* \overrightarrow{b}=\hat{i}[(-1)(5)-(1)(-3)]-\hat{j}[(2)(5)-(1)(1)]+\hat{k}[(2)(-3)-(-1)(1)]`

`\overrightarrow{a}* \overrightarrow{b}=\hat{i}[-5+3]-\hat{j}[10-1]+\hat{k}[-6+1]`

`\overrightarrow{a}* \overrightarrow{b}=-2\hat{i}-9\hat{j}-5\hat{k}`

Now the magnitude of the cross product is:

`|\overrightarrow{a}* \overrightarrow{b}|=√((-2)^2+(-9)^2+(-5)^2)`

`|\overrightarrow{a}* \overrightarrow{b}|=√(4+81+25)`

`|\overrightarrow{a}* \overrightarrow{b}|=√(110)`

Therefore, the value of
`|\overrightarrow{a}* \overrightarrow{b}|` is
`√(110)`.