Question

Find the projection of vector \(\vec{a}=8\hat{i}-\hat{j}+6\hat{k}\) on vector \(\vec{b}= 4\hat{i}+3\hat{j}\).

(a) \(\sqrt{\frac{29}{5}}\)

(b) \(\frac{29}{\sqrt{5}}\)

(c) \(\frac{\sqrt{29}}{5}\)

(d) \(\frac{29}{5}\)

The question was posed to me during an internship interview.

My question is from Product of Two Vectors-1 in division Vector Algebra of Mathematics – Class 12

Answer 1

Right choice is (d) \(\frac{29}{5}\)

For explanation: The projection of a vector \(\vec{a}\) on vector \(\vec{b}\) is given by

\(\frac{1}{|\vec{b}|} (\vec{a}.\vec{b})\)

\(|\vec{b}|=\sqrt{4^2+3^2}=\sqrt{16+9}\)=5

\(\vec{a}.\vec{b}\)=8(4)-1(3)+0=32-3=29

The projection of vector \(8\hat{i}-\hat{j}+6\hat{k}\) on vector \(4\hat{i}+3\hat{j}\) will be

\(\frac{1}{|\vec{b}|} (\vec{a}.\vec{b})=\frac{1}{5} (29)=\frac{29}{5}\)