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Q4 Find the projection of the vector \hat i + 3 \hat j + 7 \hat k  on the vector 7\hat i - \hat j + 8 \hat k

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best_answer

Let 

\vec a =\hat i + 3 \hat j + 7 \hat k

\vec b=7\hat i - \hat j + 8 \hat k

The projection of \vec a on  \vec b is 

\frac{\vec a.\vec b}{\left | \vec b \right |}=\frac{(\hat i+3\hat j+7\hat k)(7\hat i-\hat j+8\hat k)}{\left | 7\hat i-\hat j+8\hat k \right |}=\frac{7-3+56}{\sqrt{7^2+(-1)^2+8^2}}=\frac{60}{\sqrt{114}}

Hence, projection of vector \vec a on  \vec b is 

\frac{60}{\sqrt{114}}

 

 

Posted by

Pankaj Sanodiya

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