Question

If `A = <2 ,-5 ,-4 >`, `B = <-9 ,1 ,9 >` and `C=A-B`, what is the angle between A and C?

Answer 1

`pi/2`

Explanation:

Angle between two vectors U and V is given by the formula

`cos theta` = `( U . V )/(| U |.| V |)`
In the present case
U = A = <2,-5,-4> and V = C = A - B = <-11, 6, 13>
U . V= (2, -5,-4).(-11,6,-13) = -22 -30+52=0

|U|= `sqrt (2^2 +(-5)^2 +(-4)^2)` = `sqrt 45`

|V|= `sqrt (11^2 +6^2 +13^2) = sqrt(326)`

Hence `cos theta` = `0/(sqrt45 .sqrt326)`=0

Hence `theta= pi/2`