Question

The unit vector along icap+jcap+kcap is

Answer 1

To find:

The unit vector along icap+jcap+kcap

Calculation:

For a vector :

$\boxed{ \vec{v} = a \hat{i} + b \hat{j} + c \hat{k}}$

The general expression for unit vector is:

$\boxed{\hat{v} = \dfrac{ \vec{v}}{ | \vec{v}| } }$

So,in this question , the given vector is:

$\vec{v} = \hat{i} + \hat{j} + \hat{k}$

So, the unit vector will be :

$\hat{v} = \dfrac{ \vec{v}}{ | \vec{v}| }$

$= > \hat{v} = \dfrac{ \hat{i} + \hat{j} + \hat{k}}{ \sqrt{ {1}^{2} + {1}^{2} + {1}^{2} } }$

$= > \hat{v} = \dfrac{ \hat{i} + \hat{j} + \hat{k}}{ \sqrt{ 1 +1 + 1} }$

$= > \hat{v} = \dfrac{ \hat{i} + \hat{j} + \hat{k}}{ \sqrt{3} }$

So, the required unit vector:

$\boxed{ \bf{\hat{v} = \dfrac{ \hat{i} + \hat{j} + \hat{k}}{ \sqrt{3} } }}$