Find the dot product $a • b$ and the angle between the two vectors in each set. $a=\binom{3}{-1}$, $b= \binom{-1}{2}$
(note: the vector notation above is not exactly a vector notation, but it is similar...)
So I can get the product of $a • b = -3-2 = -5$. However, doing $$\cos\theta = -\frac{5}{\sqrt{10}•\sqrt{5}} = -\frac{1}{\sqrt{2}}$$ and there are two $\theta$ values that yield $-1/\sqrt{2}$, namely $3\pi/4$ and $5\pi/4$. But then the answer says it is simply $3\pi/4$. Why is that?
Let $\vec{a}=\vec{OA}$ and $\vec{b}=\vec{OB}$.
Thus, if $\vec{a}\neq\vec{0}$ and $\vec{b}\neq\vec{0}$ then the angle between $\vec{a}$ and $\vec{b}$ it's $\measuredangle AOB$ by definition.
Also, by definition of measured angle we have $0^{\circ}\leq\measuredangle AOB\leq180^{\circ}$.
Thus, in our case the answer is $135^{\circ}$.