# Couple more problems

• Jan 16th 2007, 05:16 PM
gretchen
Couple more problems
I have two problems to finish my worksheet and was hoping for some help.

First one is...find the smallest positive angle from the positive x-axis to the vector OP that corresponds to (3,3).

I think it is pi/4 since that is the smallest angle and still positive.

Second one is...determine m such that the two vectors 3i-9j and mi+2j are orthogonal.

I could apply the dot product to it but the orthogonal makes me think I may not really be thinking about it the right way.
• Jan 16th 2007, 06:09 PM
topsquark
Quote:

Originally Posted by gretchen
I have two problems to finish my worksheet and was hoping for some help.

First one is...find the smallest positive angle from the positive x-axis to the vector OP that corresponds to (3,3).

I think it is pi/4 since that is the smallest angle and still positive.

Second one is...determine m such that the two vectors 3i-9j and mi+2j are orthogonal.

I could apply the dot product to it but the orthogonal makes me think I may not really be thinking about it the right way.

You have the first one right. Good job!

And your approach to the second one is correct also. If the word "orthogonal" is confusing you, in this context it merely means "perpendicular." The dot product between two perpendicular vectors is 0. So:
$\displaystyle (3i - 9j) \cdot (mi + 2j) = 0$

$\displaystyle 3m - 18 = 0$

$\displaystyle m = 6$

-Dan