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  • Projection of vector <img alt="\overrightarrow{a}= 3\hat{i}+2\hat{j}-5\hat{k}" src="https://learn.careers360.com/latex-image/?%5Coverrightarrow%7Ba%7D%3D%203%5Chat%7Bi%7D&plus;2%5Chat%7Bj%

Projection of vector \overrightarrow{a}= 3\hat{i}+2\hat{j}-5\hat{k} on \overrightarrow{b}= -2\hat{i}+2\hat{j}+\hat{k} has length

Option: 1

\frac{4}{3}

 

 

 


Option: 2

\frac{5}{3}


Option: 3

\frac{7}{3}


Option: 4

\frac{8}{3}


Answers (1)

best_answer

As we learn

Projection of vector a on vector b -

\vec{a}\cos \Theta = \frac{\vec{a}.\vec{b}}{\left | \vec{b} \right |}

- wherein

Projection of vector a on vector b

 

 Projection of \vec{a} on \vec{b} =\frac{\vec{a}\cdot \vec{b}}{\left |\vec{b} \right |} = \frac{(3)(-2)+(2)(2)-5(1)}{\sqrt{4+4+1}}

= \frac{-7}{3}

\therefore length of projection = \frac{7}{3}

 

Posted by

avinash.dongre

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