Question

Find direction cosines of a vector $\overrightarrow{w}=-2.4\hat{i}-3\hat{j}+1.3\hat{k}$ respectively.

• A. $0.59,0.73,0.32$
• B. $0.59,0.73,-0.32$
• C. $-0.59,-0.73,0.32$
• D. $-0.59,-0.73,-0.32$

Answer 1

The correct option is C $-0.59,-0.73,0.32$

$\overrightarrow{w}=-2.4\hat{i}-3\hat{j}+1.3\hat{k}$

Direction cosines are

$(\frac{-2.4}{\sqrt{{(-2.4)}^2+{(-3)}^2+{\left(1.3\right)}^2}},\frac{-3}{\sqrt{{(-2.4)}^2+{(-3)}^2+{\left(1.3\right)}^2}},\frac{1.3}{\sqrt{{(-2.4)}^2+{(-3)}^2+{\left(1.3\right)}^2}})$

$=(\frac{-2.4}{4.05},\frac{3}{4.05},\frac{1.3}{4.05})$

$=(-.59,-.73,.32)$

So, option C is correct.