Question

A vector of magnitude $7$ units, parallel to the resultant of the vectors ${a} = 2{i}-3{j} -2{k}$ and ${b}=-{i} +2{j} +{k}$, 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 $c = a + b$
$=(2 i -3 j -2 k )+(- i +2 j + 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
$=\frac{7}{\sqrt{3}}( i - j - k )$