Find the angle alpha between the vectors

Question

Find the angle between the vectors 

[-3

 3]

and 

[-5

  5]

 

 

Answer 1

To find the angle between two vectors, you need the following theorem:

 

A•B = ||A|| ||B|| cosθ

 

That is, the dot product of 2 vectors can also be defined as the magnitude of A * magnitude of B * cosθ

 

The dot product of A and B is:

-3*-5 + 3*5

= 0

 

The magnitude of A = sqrt((-3)² + (3)²) = sqrt(18)

The magnitude of B = sqrt((-5)² + (5)²) = sqrt(50)

 

If we substitute all of that info into our equation:

 

A•B = ||A|| ||B|| cosθ

 

0 = √18 * √50 cosθ

 

Divide through by √18 * √50:

 

0 = cosθ

 

cos^-1(0) = cos^-1(cosθ)

 

cos^-1(0) = θ

 

θ = 90°