Question

What is the approximate angle between two position vectors if their terminal points are (5, -2) and (7, 3)?

Answer 1

Are you familiar with a "dot product?"

Answer 2

sort of

Answer 3

I know it but dont quite understand it

Answer 4

A dot product has two very convenient methods of calculating it's value. Given the vectors A=(a,b) and B=(c,d):

\[A . B =|A||B|Cos(\theta)\]
and
\[A.B = (a,b).(c,d) = ac+bd\]

We can equate the two methods:
\[ac+bd = |A||B|Cos(\theta)\]

And then solve for the angle, theta.

Answer 5

so like (5)(7)+(-2)(3)=cos theta?

Answer 6

Got it. Thanks!

Answer 7

Close, you dropped the |A| and |B|

These are the "magnitudes" of A and B. It's just how long they are. You can use the Pythagorean theorem to find their magnitudes:
If A = (a,b)
\[|A| = \sqrt{a^2+b^2}\]