Question

If `vec"a"` and `vec"b"` are two vectors such that `|vec"a"| = 10, |vec"b"| = 15` and `vec"a"*vec"b" = 75sqrt(2)`, find the angle between `vec"a"` and `vec"b"`

Answer 1

Given `|vec"a"| = 10, |vec"b"| = 15` and `vec"a"*vec"b" = 75sqrt(2)`

Let θ be the angle between `vec"a"` and `vec"b"`

cos θ = `(vec"a"*vec"b")/(|vec"a"| * |vec"b"|)`

= `(75sqrt(2))/(10 xx 15)`

= `sqrt(2)/2`

cos θ = `1/sqrt(2)`

cos θ = `(15 xx 5 xx sqrt(2))/(10 xx 15)`

cos θ = `sqrt(2)/(sqrt(2) xx sqrt(2))`

= `1/sqrt(2)`

θ = 45°

= `pi/4`