Question

A vector of magnitude $7$ units, parallel to the resultant of the vectors $a=2i-3j-2k$ and $b=-i+2j+k$, is

• A. $\frac{7}{\sqrt{3}}\left(i+j+\hat{k}\right)$
• B. $7\left(\hat{i}-j-k\right)$
• C. $\frac{7}{\sqrt{3}}\left(i-j+k\right)$
• D. $\frac{7}{\sqrt{3}}\left(i-j-k\right)$
• E. $7\left(i+\hat{j}-k\right)$

Answer 1

Answer: (D)

$\therefore$ Resultant vector $c=a+b$
$=(2i-3j-2k)+(-i+2j+k)$
$=(i-j-k)$
$\therefore$ Unit vector of $c$
$=\frac{i-j-k}{\sqrt{1^2+1^2+1^2}}=\left(\frac{i-j-k}{\sqrt{3}}\right)$
$\therefore$ Required vector
$=\frac{7}{\sqrt{3}}(i-j-k)$