Answer
Obtuse
Work Step by Step
We know the following:
$\cos\theta=\frac{u\cdot v}{|u||v|}$
Therefore, it follows:
$u\cdot v=1(-3)+(2)(1)+3(2)+4(-2)=-3$
$|u|=\sqrt{((1)^2+(2)^2+(3)^2+(4)^2)}=\sqrt{30}$
$|v|=\sqrt{((-3)^2+1^2+2^2+(-2)^2)}=\sqrt{18}=3\sqrt{2}$
So:
$\cos\theta=\frac{u.v}{|u||v|}=\frac{-3}{\sqrt{30}\sqrt{2}\times3}$
The value of $\cos\theta$ is between -1 and 0, so it is an obtuse angle.
