Determine the angle measure between vectors u and v: u = 4i – 2j and v = i + 3j

Question

Determine the angle measure between vectors u and v: u = 4i – 2j and v = i + 3j .

Answer 1

u = 4i – 2j and v = i + 3j

 

u·v = (4)(1) + (-2)(3) = 4 - 6 = -2

 

||u|| = √(4² + (-2)²) = √20 = 2√5

 

||v|| = √(1² + 3²) = √10

 

||u|| ||v|| = 2√5 √10 = 2√50 = 10√2

 

cos θ = u·v/(||u|| ||v||) = -2/(10√2) = -√2 / 10 ≈ -0.14142

 

θ ≈ 98.13°