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

Answer 1

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")`.