Question

The direction cosines of the vector $2 \hat{i} + \hat{j} -2 \hat{k}$ are

• 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

Answer: (A)

Let $\bar{A} = 2 \hat{i} + \hat{j} - 2 \hat{k}$
D.r.'s of vector are $< 2, 1, -2 >$
$\therefore $ Direction cosines are
$< \frac{2}{\sqrt{\left(2\right)^{2} +\left(1\right)^{2} +\left(-2\right)^{2}}} , \frac{1}{\sqrt{\left(2\right)^{2} + 1+\left(-2\right)^{2}}} , \frac{-2}{\sqrt{\left(2\right)^{2} + 1+ \left(-2\right)^{2}}} > $
$= < \frac{2}{\sqrt{9}}, \frac{1}{\sqrt{9}}, \frac{-2}{\sqrt{9}} > i.e. = < \frac{2}{3}, \frac{1}{3}, \frac{-2}{3} >$