Answer
Acute
Work Step by Step
If u and v are vectors, it follows:
$\cos\theta=\frac{u \cdot v}{|u||v|}$
Therefore, we find:
$u\cdot v=2(1)+(-1)(-2)+1(-1)=3$
$|u|=\sqrt{((2)^2+(-1)^2+1^2)}=\sqrt{6}$
$|v|=\sqrt{((1)^2+(-2)^2+(-1)^2)}=\sqrt{6}$
so $\cos\theta=\frac{u\cdot v}{|u||v|}=\frac{3}{\sqrt{6}\sqrt{6}}=\frac{3}{6}=\frac{1}{2}$
$\theta =60 \ degrees$
This is less than 90 degrees, so the angle is acute.
