Question

Find the direction cosines of the vector $\overrightarrow{v}=\overrightarrow{2i}+\overrightarrow{3j}-\overrightarrow{6k}.$

• A. $<2,3,-6>$
• B. $<-2,-3,6>$
• C. $<-\frac{2}{7},\frac{-3}{7},\frac{6}{7}>$
• D. $<\frac{2}{7},\frac{3}{7},\frac{-6}{7}>$

Answer 1

The correct option is D $<\frac{2}{7},\frac{3}{7},\frac{-6}{7}>$

Consider the unit base vector,

$\overrightarrow{v}=2\hat{i}+3\hat{j}-6\hat{k}$

Let, the direction cosines are $\cos \alpha ,\cos \beta$ and $\cos \lambda$,

Now,

$\cos \alpha =\frac{2}{\sqrt{2^2+3^3+{(-6)}^2}}=\frac{2}{7}$

$\cos \beta =\frac{3}{\sqrt{2^2+3^3+{(-6)}^2}}=\frac{3}{7}$

$\cos \gamma =\frac{-6}{\sqrt{2^2+3^3+{(-6)}^2}}=\frac{-6}{7}$

Hence, this is the answer.