Question

If $|\vec{a}| = 8$, $|\vec{b}| = 5$ and $|\vec{a} - \vec{b}| = 7$, then the angle between $\vec{a}$ and $\vec{b}$ is equal to

• A. $\dfrac{3\pi}{4}$
• B. $\dfrac{2\pi}{3}$
• C. $\dfrac{\pi}{4}$
• D. $\dfrac{\pi}{6}$
• E. $\dfrac{\pi}{3}$

Hint:

Remember: $|\vec{a}\pm\vec{b}|^2 = |\vec{a}|^2 \pm 2\vec{a}\cdot\vec{b} + |\vec{b}|^2$. This is the vector analogue of the law of cosines and is frequently tested in KEAM.

Answer 1

Answer: (E)