Question

What is the unit vector in the direction opposite to that of ixj?

Answer 1

SOLUTION

TO DETERMINE

The unit vector in the direction opposite to that of

$\hat{i} \times \hat{j}$

EVALUATION

Let the given ve

$\vec{u} = \hat{i} \times \hat{j}$

Now

$\vec{u} = \hat{i} \times \hat{j}$

$\implies \vec{u} = \displaystyle\begin{vmatrix} \hat{i} & \hat{j} & \hat{k}\\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{vmatrix}$

$\implies \vec{u} =0. \hat{i} + 0.\hat{j} + 1. \hat{k}$

$\implies \vec{u} = \hat{k}$

So

$| \vec{u} | = | \hat{k} |$

$\implies \: | \vec{u} | = \sqrt{{0}^{2} + {0}^{2} + {1}^{2} }$

$\implies \: | \vec{u} | = 1$

Hence the required unit vector

$\displaystyle \: = - \frac{\vec{u} }{| \vec{u} |}$

$= \displaystyle \: - \frac{\hat{k} }{1}$

$= \displaystyle \: - \hat{k}$

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