Finding relative coordinates of a vector

by war485
Tags: coordinates, relative, vector
war485 is offline
Jan17-09, 04:29 PM
P: 88
1. The problem statement, all variables and given/known data

I'm trying to find the coordinates of a vector [ 7 4 1 ] relative to these three vectors:
[ -1 2 -9 ] , [ 1 5 1 ] , [ 47 -8 -7 ]

2. Relevant equations


3. The attempt at a solution

Do I get all these vectors into an augumented matrix?
[ -1 1 47 | 7 ]
[ 2 5 -8 | 4 ]
[ -9 1 -7 | 1 ]
and then row reduce completely? I got very awkward numbers and just wanted to make sure I'm using the correct method.
Phys.Org News Partner Science news on
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language
HallsofIvy is offline
Jan17-09, 04:43 PM
Sci Advisor
PF Gold
P: 38,904
I take it that "relative to these three vectors" means write it as a linear combination of those vectors. What you want are three numbers, a, b, c such that
a<-1, 2, 9>+ b<1, 5, 1>+ c<47, -8, -7>= <7, 4, 1>. Looking at x, y, and z components separately that means -a+ b+ 47c= 7, 2a+ 5b- 8c= 4, 9a+ b- 7c= 1 which gives exactly the augmented matrix you have.

Are you sure about that "47"? That number looks out of place.
war485 is offline
Jan17-09, 04:47 PM
P: 88
yes that 47 must be there because it was part of another question where I had to find a third vector orthogonal to the other two (involving the cross product) and I'm confident about that.

If you say that my setup is right, then my more awkward numbers must be right.
I got
a = -4/43
b = 28/27
c = 145/1161

war485 is offline
Jan17-09, 05:02 PM
P: 88

Finding relative coordinates of a vector

oups, I made a mistake and it'll affect my a b c values. But thanks for confirming my method Ivy.

Register to reply

Related Discussions
Vector Addition using coordinates Introductory Physics Homework 1
Vector in spherical coordinates Calculus 0
polar vector coordinates General Math 4
CM and Relative Coordinates; Reduced Mass Advanced Physics Homework 1
Coordinates of vector to the base Linear & Abstract Algebra 2