# Vectors!

• Feb 27th 2013, 12:19 AM
Tutu
Vectors!
1.) P(-1,2,3) and Q(4,0,1) are two points in space. Find the angle that PQ makes with the X-axis.

I got PQ to be (5,-2,-4). I know to use the formula for the angle between two vectors but I'm having trouble with the x-axis part. I know it is k(1,0,0), where k is a parameter. Since (1,0,0) is a direction on the x-axis, to have a line, k would be a parameter.
But with this unknown parameter, how am I to solve for the angle?

2.) Given P(2,-5,6) and Q(-1,7,9), find the distance from P to the x-axis.
Again the parameter problem, I can solve it without the parameter, so how should I go about this question?

3.) For A(2,-1,3) and B(0,1,-1), find the coordinates of C on AB which is 2 units from A.

How do I do this? I know it is something to do with ratio but I'm not sure..

Thank you so much!
• Feb 27th 2013, 12:40 AM
Prove It
Re: Vectors!
1. You need to use the definition of the dot product: \displaystyle \displaystyle \begin{align*} \mathbf{a} \cdot \mathbf{b} = \left| \mathbf{a} \right| \left| \mathbf{b} \right| \cos{\left( \theta \right)} \end{align*}.

2. Why would you be given Q if you are just finding the distance between P and the x axis? Did you write this question correctly?
• Feb 27th 2013, 02:52 AM
Tutu
Re: Vectors!
Hi thank you for your reply! For 1.) I know to use the dot product but please how do I do it? I really am unsure of what to do with the parameter since the x axis is k(1,0,0) where k is a parameter! For2.) I copied the question correctly, it is just that there are other parts to this question that involves Q that I know how to do this I didn't put them down.
• Feb 27th 2013, 03:41 AM
Plato
Re: Vectors!
Quote:

Originally Posted by Tutu
Hi thank you for your reply! For 1.) I know to use the dot product but please how do I do it? I really am unsure of what to do with the parameter since the x axis is k(1,0,0) where k is a parameter!

Do nothing with it.
The answer is simply $\displaystyle \arccos \left( {\frac{{\overrightarrow {PQ} \cdot i}}{{\left\| {\overrightarrow {PQ} } \right\|}}} \right)$
• Feb 27th 2013, 04:10 AM
Tutu
Re: Vectors!
Is there a value.for i? Like 1 or something
• Feb 27th 2013, 04:24 AM
Plato
Re: Vectors!
Quote:

Originally Posted by Tutu
Is there a value.for i? Like 1 or something

$\displaystyle i=<1,0,0>$.