Vectors: orthogonal / opposite

• Apr 20th 2009, 04:28 PM
laser
Vectors: orthogonal / opposite
x=<3, 2, -4>
y=<-3/2, 1, -2>
z=<0, 2, 1>

Which of these statements apply?

1. vectors x and y are orthogonal
2. vectors x and y are in opposite directions
3. vectors x amd z are orthogonal
4. vectors x and z are in opposite directions
• Apr 21st 2009, 01:36 AM
charlie
If two vectors are orthogonal (ie. perpendicular to each other), then their dot product will be zero, because the angle between them is 90 degrees. You could use this to either rule out two of them or find your answer.

dot product:
<a,b,c> . <d,e,f> = (a x d) + (b x e) + (c x f)
• Apr 22nd 2009, 04:38 PM
laser
It seems like c is the only statement that applies since the dot product of a and z equals 0. I don't think any of the vectors are opposites of another since there does not exist a negative scalar that would make one vector equal another. Is this the correct way to compute opposites?
• Apr 22nd 2009, 04:48 PM
Gamma
Dot Product
$\displaystyle |\vec{v_1}||\vec{v_2}|cos(\theta)=v_1\cdot v_2$

This might be of some use as you can solve for $\displaystyle \theta$ which is the angle between the vectors.

$\displaystyle \theta=arccos\left(\frac{v_1\cdot v_2}{|\vec{v_1}||\vec{v_2}|}\right)$
• Apr 23rd 2009, 05:05 AM
charlie
I'd say two vectors are opposite if they're parallel but their directions are opposite. ie. (x,y,z) and (-ax,-ay,-az), where a is any positive real number and x, y and z are any real numbers, positive or negative. That's what you had in mind, yeah? So with that definition, I'd say you're correct thinking that c is the only true statement :)
• May 14th 2009, 08:38 AM
amburden
Test Question
This is a test question and my student had no business posting it here!
Dr. B
• May 31st 2009, 05:22 AM
Jameson
Quote:

Originally Posted by amburden
This is a test question and my student had no business posting it here!
Dr. B

Thread closed while this is reviewed.