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
$<\frac{2}{\sqrt{{\left(2\right)}^2+{\left(1\right)}^2+{\left(-2\right)}^2}},\frac{1}{\sqrt{{\left(2\right)}^2+1+{\left(-2\right)}^2}},\frac{-2}{\sqrt{{\left(2\right)}^2+1+{\left(-2\right)}^2}}>$
$=<\frac{2}{\sqrt{9}},\frac{1}{\sqrt{9}},\frac{-2}{\sqrt{9}}>i.e.=<\frac{2}{3},\frac{1}{3},\frac{-2}{3}>$