Finding relative coordinates of a vector

• war485
In summary, the conversation involved finding the coordinates of a vector relative to three given vectors and discussing the method of setting up an augmented matrix and solving for the coefficients. The output of this method resulted in the values a = -4/43, b = 28/27, and c = 145/1161.
war485

Homework Statement

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 ]

none

The Attempt at a Solution

Do I get all these vectors into an augumented matrix?
like:
[ -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.

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.

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

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

Last edited:

1. What are relative coordinates of a vector?

Relative coordinates of a vector refer to the position of the vector relative to a specific reference point or coordinate system.

2. How do you find the relative coordinates of a vector?

To find the relative coordinates of a vector, you need to determine the distance and direction of the vector from the reference point using mathematical calculations.

3. Can relative coordinates of a vector be negative?

Yes, relative coordinates of a vector can be negative if the vector is positioned in the opposite direction of the reference point.

4. What is the difference between absolute and relative coordinates of a vector?

The absolute coordinates of a vector refer to its position in a fixed coordinate system, while relative coordinates refer to its position relative to a specific reference point or coordinate system.

5. How are relative coordinates of a vector used in real life?

Relative coordinates of a vector are commonly used in navigation, engineering, and physics to determine the position of objects in relation to a fixed point or coordinate system.

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