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) = (1^{2} + 2^{2} + 5^{2})^{1/2}.(2^{2} + 1^{2} + 4^{2})^{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}

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