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

(2\(\hat{i}\) + 2\(\hat{j}\)+ 3\(\hat{k}\))/√17 

The given points are P(1,3,5) and Q(3,5,8)

\(\vec{PQ}\) = (3-1)\(\hat{i}\) + (5-3)\(\hat{j}\)+ (8-5)\(\hat{k}\)

\(\vec{PQ}\) = 2\(\hat{i}\) + 2\(\hat{j}\)+ 3\(\hat{k}\)

Magnitude of \(\vec{PQ}\) = |\(\vec{PQ}\)|=√{(2)² +(2)² +  (3)²}

Magnitude of \(\vec{PQ}\)= √17

Hence the unit vector in direction of  \(\vec{PQ}\)  = \(\vec{PQ}\)/|\(\vec{PQ}\)| = (2\(\hat{i}\) + 2\(\hat{j}\)+ 3\(\hat{k}\))/√17