Question

The vector $\vec{a}=-\hat{i}+2 \hat{j}+\hat{k}$ is rotated through a right angle, passing through the y-axis in its way and the resulting vector is $\vec{b}$. Then the projection of $3 \vec{a}+\sqrt{2} \vec{b}$ on $\vec{c}=5 \hat{i}+4 \hat{j}+3 \hat{k}$ is :

• A. $3 \sqrt{2}$
• B. 1
• C. $2 \sqrt{3}$
• D. $\sqrt{6}$

Answer 1

Answer: (A)

$3 \sqrt{2}$

Answer 2

b=λa×(a×j^​)
⇒b=λ(−2i^−2j^​+2k^)
∣b∣=∣a∣∴6​=12​∣λ∣⇒λ=±2​1​
(λ=2​1​ rejected ∵b makes acute angle with y axis )
b=−2​(−i^−j^​+k^)
$\frac{(3a+2b)-c}{|c|}=3\sqrt2$