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So I'm not sure how to solves these problems. The Question asks to Determine whether the given vectors are orthogonal, parallel or neither.

1) a = <-5, 3, 7> and b = <6, -8, 2>

2) a = <4, 6> and b = <-3, 2>

So I understand that I have to find the angle between the two vectors. And that will determine what is it. So for the first one, I got an angle of 115.5 Degrees. But now how do I know where that falls into?

I'm also assuming that orthogonal is perpendicular? Which means that the angle is 90 degrees or pi/2 radians.

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$a\cdot b=|a||b|\cos(\theta)$ so $a\cdot b=0$ implies orthogonal/perpendicular/at right angles to one another. parallel means on is a scalar multiple of the other. – yoyo Sep 2 '12 at 2:53
up vote 2 down vote accepted

You have the definitions a bit mixed up. You mentioned that you know how to find the angle between vectors.

Recall that orthogonal vectors are also called perpendicular vectors, meaning the angle between the two must be $90^\circ$.

On the other hand, parallel vectors lie on a straight-line, so the angle between the vectors is either $0^\circ$ (if they point the same way) or $180^\circ$ (if they point opposite ways).

With this information in mind, if two vectors are seperated by an angle of $115.5^\circ$ then are they parallel? Orthogonal?

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Yea, I noticed I had the definitions mixed up. I fixed it. So #1 is Neither because it is past 90 degrees? Also what makes a vector parallel? Is having an angle of 0 and 180 parallel? – Avalon-96 Sep 2 '12 at 2:52
@Avalon-96: yes, vectors with angles of $0^\circ$ and $180^\circ$ are parallel. Sometimes we differentiate in the same sense (or direction) and the opposite sense. – Ross Millikan Sep 2 '12 at 2:57

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