Question

If $p=i-2 j+3 k$ and $q=3 i+j+2 k$, than a vector $r$ which is linear combination of $p$ and $q$ and also perpendicular to $q$ is

• A. $i+5 j-4 k$
• B. $i-5 j+4 k$
• C. $\frac{-1}{2}(i+5 j-4 k)$
• D. none of these

Answer 1

Answer: (C)

We have, $r=p+\lambda q$
$\Rightarrow r \cdot q=p \cdot q+\lambda q \cdot q $
$\therefore 0=7+14 \lambda $
$(\because p \cdot q=3-2+6=7 $ and $ q \cdot q=9+1+4=14) $
$\Rightarrow \lambda=-\frac{7}{14}=-\frac{1}{2} \cdot $
$\therefore r=-\frac{1}{2}(i+5 j-4 k)$