Question

The projection of the vector $2i+aj-\hat{k}$ on the vector $\hat{i}-2j+\hat{k}$ is $\frac{-5}{\sqrt{6}}$ . Then, the value of $a$ is equal to

• A. 1
• B. 2
• C. $-2$
• D. 3
• E. $-3$

Answer 1

Answer: (D)

Let $a=2i+aj-k$ and $b=i-2j+k$ the projection of a on b is
$=\frac{a.b}{|b|}$ $\because$ $\frac{-5}{\sqrt{6}}=\frac{(2i+aj-k).(i-2j+k)}{\sqrt{1+4+1}}$
$\Rightarrow$ $\frac{-5}{\sqrt{6}}=\frac{2-2a-1}{\sqrt{6}}$
$\Rightarrow$ $-2a+1=-5$
$\Rightarrow$ $2a=6$
$\Rightarrow$ $a=3$