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Find the unit vector in the direction of...

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.

Text Solution

Verified by Experts

The given points are `P(1,2,3) and Q(4, 5, 6)`. Therefore,
`" "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)=sqrt(27)=3sqrt(3)`
Hence, the unit vector in the direction of `vec(PQ)` is
`" "(vec(PQ))/(|vec(PQ)|)=(3hati+3hatj+3hatk)/(3sqrt(3))=(1)/(sqrt(3))hati+(1)/(sqrt(3))hatj+(1)/(sqrt(3))hatk`
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