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  • Find the unit vector in the direction of vector PQ, where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.

Q.8     Find the unit vector in the direction of vector \vec { PQ} , where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.

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Given P =  (1, 2, 3) and Q = (4, 5, 6)

A vector in direction of PQ 

\vec {PQ}=(4-1)\hat i+(5-2)\hat j +(6-3)\hat k

\vec {PQ}=3\hat i+3\hat j +3\hat k

Magnitude of PQ

\left | \vec {PQ} \right |=\sqrt{3^2+3^2+3^2}=3\sqrt{3}

Now, unit vector in direction of PQ 

\hat u=\frac{\vec {PQ}}{\left | \vec {PQ} \right |}=\frac{3\hat i+3\hat j+3\hat k}{3\sqrt{3}}

\hat u=\frac{\hat i}{\sqrt{3}}+\frac{\hat j}{\sqrt{3}}+\frac{\hat k}{\sqrt{3}}

Posted by

Pankaj Sanodiya

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