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
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1 Answers
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}