# Simple vector arithmetic question

1. Dec 28, 2013

### The_Engineer

I have two vectors: a = <ax, ay, az> and c = <cx, cy, cz>

which have an angle of 45 degrees between them.

If I get another vector by b = c - a then shouldn't b be orthogonal to a? I'm assuming this since a + b = c

Last edited: Dec 28, 2013
2. Dec 28, 2013

### A.T.

Did you try to sketch some vectors and to come up with a counter example?

3. Dec 28, 2013

### The_Engineer

Yes I have been using MATLAB to sketch and generate random examples. Here is one...

a = <0.3814, 0.9023, 0.2010>
c = <0.3965, 0.7378, -0.5463>

The angle between these vectors is 45 degrees.

I want a vector b such that b is orthogonal to a AND 45 degrees from c. Graphically speaking, this means a + b = c

Solving for b,
b = c - a = <0.0151, -0.1645, -0.7473>.

But b dot a ≠ 0 therefore they aren't orthogonal. Why aren't a and b orthogonal?

This happens for every random sample I make, starting with 2 vectors that are 45 degrees apart.

4. Dec 28, 2013

### The_Engineer

Nevermind I figured it out... I made a mistake by normalizing the resultant, which in turn messed up my final answer.

5. Dec 29, 2013

### mathman

The vectors you describe will form a triangle. With one angle at 45 deg. the other two angles could be anything that add up to 135 deg.