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Question
If A(1, 2, – 3) and B(– 1, – 2, 1) are the end points of a vector `vec("AB")` then find the unit vector in the direction of `vec("AB")`.
Solution
`vec("AB")` = P.V. of B – P.V. of A
= (– 1, – 2, 1) – (1, 2, – 3)
= (– 1 – 1, – 2 – 2, 1 + 3)
= (– 2, – 4, 4)
= `-2hat"i" - 4hat"j" + 4hat"k"`
`|vec("AB")| = sqrt((-2)^2 + (-4)^2 + 4^2)`
= `sqrt(4 + 16 + 16)`
= `sqrt(36)`
= 6
∴ Unit vector along
`vec("AB") = vec("AB")/|vec("AB")|`
= `(-2hat"i" - 4hat"j" + 4hat"k")/6`
= `(-1)/3(hat"i" + 2hat"j" - 2hat"k")`
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