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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"`
Solution
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`
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