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