Question

$If\overrightarrow{a}=(3,-2,1),\overrightarrow{b}=(-1,1,1)$ then the unit vector parallel to the vector $\overrightarrow{a}+\overrightarrow{b}$ is

• A. $(\frac{2}{3},-\frac{1}{3},\frac{2}{3})$
• B. $(\frac{2}{5},-\frac{1}{5},\frac{2}{5})$
• C. $(\frac{2}{\sqrt{3}},-\frac{1}{\sqrt{3}},\frac{2}{\sqrt{3}})$
• D. $(-\frac{2}{\sqrt{3}},\frac{1}{\sqrt{3}},-\frac{2}{\sqrt{3}})$

Answer 1

The correct option is A $(\frac{2}{3},-\frac{1}{3},\frac{2}{3})$

$\overrightarrow{a}+\overrightarrow{b}=(3,-2,1)+(-1,1,1)=(2,-1,2)$ $\Rightarrow |\overrightarrow{a}+\overrightarrow{b}|=\sqrt{4+1+4}=\sqrt{9}=3$
Unit vector parallel to $\overrightarrow{a}+\overrightarrow{b}$ is $\pm \frac{a+b}{|\overrightarrow{a}+\overrightarrow{b}|}=\pm \frac{(2,-1,2)}{3}=(\frac{2}{3},-\frac{1}{3},\frac{2}{3})$