Question

If direction cosines of a vector of magnitude $3$ are $\frac {2}{3},-\frac {1}{3},\frac{2}{3}$ and $a > 0,$ then vector is

• A. $2i + j + 2k$
• B. $2i - j + 2k$
• C. $i -2 j +2 k$
• D. $i+2 j+2 k$

Answer 1

Answer: (B)

Unit vector with direction cosine $\frac{2}{3},-\frac{1}{3}, \frac{2}{3}$ is given by
$\hat{a}=\frac{2}{3} \hat{ i }-\frac{1}{3} \hat{ j }+\frac{2}{3} \hat{ k }$
Thus vector with magnitude 3 and direction cosine as above is given by
$3 \hat{a}=2 \hat{ i }-\hat{ j }+2 \hat{ k }$