The value of $\lambda$ when the projection of $\vec{a}=\lambda \hat{i}+\hat{j}+2 \sqrt{5} \hat{k}$ on $\vec{b}=2 \hat{i}+4 \hat{j}+\sqrt{5} \hat{k}$ is 6, is:

8

The correct answer is Option (4) → 8

projection of $\vec a$ on $\vec b$ = $|\vec a|\cos θ$

$=\frac{\vec a.\vec b}{|\vec b|}=6$

$⇒\frac{2λ+4+10}{\sqrt{5+4+16}}=6$

$⇒\frac{2(λ+7)}{\sqrt{25}}=6$

$(λ+7)=\frac{6×5}{2}$

$λ=15-7⇒λ=8$