# Simple vector arithmetic question

by The_Engineer
Tags: arithmetic, simple, vector
 P: 16 I have two vectors: a = and c = 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
 P: 4,065 Did you try to sketch some vectors and to come up with a counter example?
P: 16
 Quote by A.T. Did you try to sketch some vectors and to come up with a counter example?
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.

 P: 16 Simple vector arithmetic question Nevermind I figured it out... I made a mistake by normalizing the resultant, which in turn messed up my final answer.
 Sci Advisor P: 6,077 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.

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