More Vectors: find angle, given (p-3q) (dot) (p-3q) = 7

[Knight93]

Vector p and Vector q are unit vectors where:
(p-3q) (dot) (p-3q) = 7
Find the angle between Vector p and Vector q.

I need some brushing up on my vector skills. Any help would be nice!

Thankyou

 

[tkhunny]

Have you any Distributive Properites with that Dot Product?

Don't forget these are Unit Vectors.

 

[Knight93]

Well

Okay, well i actually got a decent start, and than i hit a wall...

Heres where i left off:

(p-3q) (dot) (p-3q) = 7
lpl^2 - 6q (dot) p + 9lql^2 = 7

At this point, I'm a bit confused on what to do with the p magnitude and q magnitude at the beginning and end of the equation above. I know that to find the angle i would just sub in --> lql lpl cos (theta) for the q (dot) p to bring in an angle. I just need help elimintaing those 2 magnitudes at the end and beginning.

Does this make sence???

Thankyou

 

[tkhunny]

Good work on the multiplication.

You didn't take my hint. What's the magnitude of a UNIT vector?

 

[Knight93]

The magnitude of a unit vector is 1... hmm...

Haha wowww!!
How did i not see that. I guess the fact it was p's and q's rather than i's, j's and k's which im more used to as unit vectors. So those magnitudes just become 1 than.

So I beleive the answer is 60 degrees than.

Thanks a lot!