The value of $\lambda $, for which the projection of $\vec{a}=\lambda \hat{i} + \hat{j} + 4\hat{k}$ on $\vec{b}=2\hat{i}+6\hat{j}+3\hat{k}$ is 4 units

8 10 11 5

5

The correct answer is Option (4) → 5 $\vec{a}$ projection on $\vec b$ = $\frac{\vec a.\vec b}{|\vec b|}=\frac{2λ+6+12}{\sqrt{4+36+9}}=4$ $⇒\frac{2(λ+9)}{7}=4$ $⇒λ+9=14⇒λ=5$