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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. |
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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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