Find the angle between the vectors

Question

Find the angle between the vectors 

[1

 4

-5]

 

and

[5

-5

4]

Answer 1

Use A·B = |A||B|cos(θ) where A and B are vectors and A·B = A_xB_x + A_yB_y + A_zB_z (dot product).

 

 

A·B = (1)(5) + (4)(-5) + (-5)(4) = -35

 

 

|A| = √(1² + 4² + (-5)²) = √42

 

|B| = √(5² + (-5)² + 4²) = √66

 

 

So, cos(θ) = -35 / (√42√66)

 

θ = cos^-1[-35/(√42√66)] = 131.7°