Associated Topics || Dr. Math Home || Search Dr. Math

### Angle Between Vectors

```Date: 06/07/2002 at 10:06:56
From: Rob Sears
Subject: Angle between two vectors, clockwise direction about a normal
vector with known direction

I have two vectors in a plane, say A and B.  I also have the normal
vector to the plane made by A and B, say vector C (which obviously
has an associated specific direction - being a vector).

I know that the angle between the two vectors A and B can be
evalulated using the dot product,

Angle = acos((A.B)/(Mod(A)Mod(B)))

but I need to know the clockwise angle from vector A to vector
B when viewed in the direction of the normal vector C, not just the
basic angle between A and B.

Best Regards
Rob Sears
```

```
Date: 06/08/2002 at 11:10:45
From: Doctor Douglas
Subject: Re: Angle between two vectors, clockwise direction about a
normal vector with known direction

Hi, Rob,

Thanks for submitting your question to the Math Forum.

Here's the algorithm: Since C points perpendicular to A and B,
it points either parallel or antiparallel to the vector cross
product A x B.

If C points parallel to A x B, then the clockwise angle, when
viewed ALONG the direction of C, is just the Angle that you
calculated above.

If C points antiparallel to A x B, then the clockwise angle is
360 deg - Angle.

This assumes that you are using right-hand-rule conventions for
the cross product.

- Doctor Douglas, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 06/10/2002 at 11:45:47
From: Rob Sears
Subject: Thank you

Doctor Douglas,

assistance was very much appreciated.

it would be of assistance to others.

Best Regards,
Rob Sears
```
Associated Topics:
College Linear Algebra
High School Linear Algebra

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search