Question 135
We are given two vectors of equal length $\frac{1}{3} \vec{a}+\vec{b}$ and $\frac{2}{3} \vec{a}+\vec{b}$, where $\vec{a}$ and $\vec{b}$ are nonzero vectors such that $|\vec{a}|=\sqrt{3}|\vec{b}|$.
a) Compute the size of the angle between the vectors $\vec{a}$ and $\vec{b}$.
b) Compute the size of the angle between the vectors $\frac{1}{3} \vec{a}+\vec{b}$ and $\frac{2}{3} \vec{a}+\vec{b}$.
a) Compute the size of the angle between the vectors $\vec{a}$ and $\vec{b}$.
b) Compute the size of the angle between the vectors $\frac{1}{3} \vec{a}+\vec{b}$ and $\frac{2}{3} \vec{a}+\vec{b}$.