Find ‘λ’ when the projection of vector(a)=λ hat(i)+hat(j)+4 hat(k)

Question

Find ‘λ’ when 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 1

We know that projection of \(\vec{a}\) on \(\vec{b}\) \(=\frac{\vec{a}.\,\vec{b}}{|\vec{b}|}\)

Putting in (i), we get

\(4=\frac{2\lambda + 18}{7}\)

\(\implies 2\lambda=28-18\)

\(\implies \frac{10}{2}=5.\)