Theory question 108
VectorsGiven that x = (−4, 3) and y = (−9, −15) (column vectors), calculate, correct to the nearest degree, the angle between the vectors.
Show the model answer
Model answer
x·y = 36 − 45 = −9.
|x| = 5, |y| = √306 ≈ 17.49.
cos θ = −9/(5 × 17.49) ≈ −0.1029, so θ ≈ 96°.
Explanation
cos θ = x·y/(|x||y|); a negative cosine means an obtuse angle.