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Question
Find a unit vector in the direction of `vec"PQ"`, where P and Q have co-ordinates (5, 0, 8) and (3, 3, 2), respectively
Solution
Given coordinates are P(5, 0, 8) and Q(3, 3, 2)
∴ `vec"PQ"` = `(3 - 5)hat"i" + (3 - 0)hat"j" + (2 - 8)hat"k"`
= `-2hat"i" + 3hat"j" - 6hat"k"`
∴ Unit vector in the direction of `vec"PQ" = vec"PQ"/|vec"PQ"|`
= `(-2hat"i" + 3hat"j" - 6hat"k")/sqrt((-2)^2 + (3)^2 + (-6)^2)`
= `(-2hat"i" + 3hat"j" - 6hat"k")/sqrt(4 + 9 + 36)`
= `(-2hat"i" + 3hat"j" - 6hat"k")/sqrt(49)`
= `(-2hat"i" + 3hat"j" - 6hat"k")/7`
= `1/7 (-2hat"i" + 3hat"j" - 6hat"k")`
Hence, the required unit vector is `1/7 (-2hat"i" + 3hat"j" - 6hat"k")`.
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