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Question
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.
Solution
Vector joining the points P, Q (1, 2, 3), (4, 5, 6) respectively,
`vec(PQ) = (4 - 1)hati + (5 - 2)hatj + (6 - 3)hatk`
`= 3hati + 3hatj + 3hatk`
`|vec(PQ)| = sqrt(3^2 + 3^2 + 3^2)`
`= sqrt(9 + 9 + 9)`
`= sqrt27`
`= 3sqrt3`
The unit vector PQ which is along PQ.
`(vec(PQ))/(|vec(PQ)|) = (3hati + 3hatj + 3hatk)/(3sqrt3)`
`= 1/sqrt3hati + 1/sqrt3hatj + 1/sqrt3hatk`
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