Find the angle between the vectors A=i^-2j^-5k^ and B=2i^+j^-4k^

A = i - 2j - 5k

B = 2i + j - 4k

now, we know that

A.B = |A||B|Sinθ

or

( i - 2j - 5k).( 2i + j - 4k) = (1² + 2² + 5²)^1/2.(2² + 1² + 4²)^1/2 Sinθ

or

2 - 2 + 20 = 5.477 x 4.582 Sinθ

thus, the angle between the two vectors will be given as

Sinθ = 20 / 25.0956

or

θ = sin^-1 (0.7969)

thus,

θ = 52.835^o