The magnitude of two vectors u and v are 10N and 12N respectively. If the magnitude of their resultant is 15N, calculate the angle between them.
Explanation
From the diagram above, using cosine's law
Cos \(\theta\) = \(\frac{10^2 + 12^2 - 15^2}{2 \times 10 \times 12}\)
Cos \(\theta\) = \(\frac{100 + 144 - 225}{2 \times 10 \times 12}\) = \(\frac{244 - 225}{240}\)
= \(\frac{19}{240}\) = 0.0791667
\(\theta\) = Cos\(^{-1}\)(0.0791667) = 85.459º
But the angle between the two vectors = 180º - \(\theta\) = 180º - 85.459º = 94.54º