# 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}.

Category: QuestionsFind the projection of vector \vec{a}=8\hat{i}-\hat{j}+6\hat{k} on vector \vec{b}= 4\hat{i}+3\hat{j}.
Editor">Editor Staff asked 11 months ago

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
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options
Interview Questions and Answers, Database Interview Questions and Answers for Freshers and Experience

Editor">Editor Staff answered 11 months ago

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}