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. $i-2j+2k$
• D. $i+2j+2k$

Answer 1

Answer: (B)

$2i-j+2k$

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

$3\hat{a}=2\hat{i}-\hat{j}+2\hat{k}$