Question

The direction cosines of the vectors $2\overrightarrow{i}+\overrightarrow{j}-2\overrightarrow{k}$ is equal to

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

Answer 1

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

We know, $\frac{a_1}{\left|a\right|},\frac{a_2}{\left|a\right|},\frac{a_3}{\left|a\right|}$ are the direction cosines of $a_{1}i+a_{2}j+a_{3}k$

Given vector is $2\hat{i}+\hat{j}-2\hat{k}$

$|a|=\sqrt{2^2+1^2+2^2}=\sqrt{9}=3$

Thus their direction cosines are $\frac{2}{3},\frac{1}{3},-\frac{2}{3}$

So, option A is correct.