Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Rotating Vectors

Date: 12/14/95 at 12:14:7
From: Anonymous
Subject: 3D Geometry? Projection?

I do not even know how to ask this question because I do not know the
names of things or concepts. I don't know where to start...

... but it is this:

	If I were a vector, say [2,3,4], and I wanted to turn to face
	another vector, say [-1,10,11], how would I do it? What would
	I be doing ?

I hope you can help me because this REALLY bugs me...

Thanks in advance,

Date: 7/28/96 at 20:36:6
From: Doctor Jerry
Subject: Re: 3D Geometry? Projection?

Any two non-zero, non-collinear vectors issuing from the same point 
form a plane. In this plane, there is an angle t between the two 
vectors.  If we use the standard convention, 0 < t < pi.  

It may be that you are asking how to rotate one vector so that it 
falls along the same line as the other.  If so, I can tell you how to 
calculate the angle between the two vectors you gave.  Use the law of 
cosines on the triangle defined by the origin and the ends of the two 

The lengths of the vectors are sqrt(29) and sqrt(222).  The length of 
the side opposite the angle t is sqrt(107).  So, from the law of 

107 = 222 + 29 - 2*sqrt(222)*sqrt(29)*cos(t).

Solving for cos(t),
cos(t) = 0.89733...
Hence, t = 0.457091... (radians) or 26.189409... (degrees).

-Doctor Jerry,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
Associated Topics:
College 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

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994-2015 The Math Forum