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Find the unit vector in the direction o...

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.

A

`hati/sqrt3+hatj/sqrt2+hatk/sqrt2`

B

`hati/sqrt2+hatj/sqrt3+hatk/sqrt3`

C

`hati/sqrt2+hatj/sqrt2+hatk/sqrt2`

D

`hati/sqrt3+hatj/sqrt3+hatk/sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
D
`vec(pq)=(4-1)hati+(5-2)hatj+(6-3)hatk`
=`3hati+3hatj+3hatk`
`hat(pq)=vec(pq)/(|pq|)`
=`(3hati+3hatj+3hatk)/(3sqrt3)`
=`hati/sqrt3+hatj/sqrt3+hatk/sqrt3`
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