Question

For given vectors,$\vec{a}=2\hat i \hat j+2\hat k$ and $\vec{b}=-\hat i + \hat j-\hat k$ , find the unit vector in thedirection of the vector $\vec{a}+\vec{b}$.

Answer 1

Solution:

To find the unit vector in direction of

$\vec{a}+\vec{b}$

Given :

$\vec{a}=2\hat i +\hat j+2\hat k$

$\vec{b}=-\hat i + \hat j-\hat k$

$\vec{a} +\vec{b} =2\hat i + \hat j+2\hat k-\hat i + \hat j-\hat k \\ \\ \vec{a} +\vec{b} = \hat i + 2\hat j+\hat k$
unit vector in the direction of $\vec{a}+\vec{b}$

$= \frac{1}{ \sqrt{6} } \hat i + \frac{2}{ \sqrt{6} } \hat j + \frac{1}{ \sqrt{6} } \hat k$
Hope it helps you.