Theory question 107
VectorsThe magnitude of two vectors u and v are 10 N and 12 N repectively. If the magnitude of their resultant is 15 N, calculate the angle between them.
Show the model answer
Model answer
|u + v|² = |u|² + |v|² + 2|u||v| cos θ.
225 = 100 + 144 + 240 cos θ, so cos θ = −19/240 = −0.0792.
θ ≈ 94.5°.
Explanation
Use the parallelogram (cosine) rule for the resultant.