1.

Findthe unit vector in the direction of vector ` -> P Q`,where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.

Answer» We have,
p.v. of `A = (hati + 2hatj + 3hatk)` and p.v.`B = (4hati + 5hatj + 6hatk)`.
`:. vec(AB) = (p.v. of B) - (p.v. of A)`
`= (4hati + 5hatj + 6hatk) - (hati + 2hatj + 3hatk) = (3hati + 3hatj + 3hatk)`. And
`|vec(AB)| = sqrt(3^(2) + 3^(2) + 3^(2)) = sqrt(27)`.
`:.` unit vector in the direction `vec(AB)` .
`= (vec(AB))/(|vec(AB)|) = (3hati + 3hatj + 3hatk)/(sqrt(27)) = (3(hati + hatj + hatk))/(3sqrt(3)) = ((hati + hatj + hatk))/(sqrt(3))`
`= (1/(sqrt(3))hati + 1/(sqrt(3))hatj + 1/(sqrt(3))hatk)`.


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