Pleaseeeee pleaseeee helppppppppp

Question

asked Apr 5, 2022 171k views

1 Answer

Blurry Sterk · Answer 1 · 2022-04-10T01:37:44+0000

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
.