Is the Angle Between Vectors [2, 1] and [1, -3] Obtuse?

[Math9999]

Homework Statement

Determine whether the angle between u=[2, 1] and v=[1, -3] is acute, obtuse, or a right angle.

Homework Equations

None.

The Attempt at a Solution

a*b=2*1+1(-3)=2+(-3)=-1, since the answer is negative, it means the angle is obtuse, am I right? Or is this even the right way of doing this problem? If not, then please correct me.

 

[andrewkirk]

That's correct.
Another way to do it is to swap the x and y coordinates of one vector and make one of them negative. That gives you a vector at right angles to the original. Drawing that new vector and comparing it to the second vector will make it easy to see whether the angle between u and v is acute, right or obtuse.

 

[Math9999]

So the answer is obtuse?