# Thread: Converting a Vector equation to a linear equation

1. ## Converting a Vector equation to a linear equation

Here is a question from an assignment I am working on. The vector equation is easy.

it is X = (1,2,1) + s(-3,-1,2) + t(3,-5,3).

Everytime I try to get a linear equation out of it, I can get several equations, so I am not sure I am doing it right.

My answer works out to be 7x+15y+18z = 125

Can someone help me with this? Is my final answer correct?

2. ## Re: Converting a Vector equation to a linear equation

Hey lukasaurus.

By using Octave, I get a reduced system:

>> >> X = [1,2,1; -2,1,3; 4,-3,4]
X =

1 2 1
-2 1 3
4 -3 4

>> rref(X)
ans =

1 0 0
0 1 0
0 0 1

3. ## Re: Converting a Vector equation to a linear equation

Thanks, but I am not sure how this confirms my answer to be correcT?

edit : it isn't correct - the last value - 125, should have been 55. I must have done a miscalc somewhere.

4. ## Re: Converting a Vector equation to a linear equation

Originally Posted by lukasaurus

Here is a question from an assignment I am working on. The vector equation is easy.
Having taught this material for many years, I do not like your approach.
Here is mine. Let $R=(x,y,x)$. Then your plane is
$\left[ {\overrightarrow {AB} \times \overrightarrow {AC} } \right] \cdot \left( {R - C} \right) = 0$

5. ## Re: Converting a Vector equation to a linear equation

Unfortunately, the assignment requires me to use the method taught for both the vector and linear equations. I'm new to this. I got an A on the summer school paper and I haven't done maths for about 10 years (as a subject at least), so all the terminology is new. This is a Level 1 paper (first year) on Linear Algebra and Vectors. I don't really understand what your method is saying?

6. ## Re: Converting a Vector equation to a linear equation

Lukasaurus, Plato is absolutely right. That approach is logical and easy to understand. once one gets vector equation one can easily find the linear equation.

7. ## Re: Converting a Vector equation to a linear equation

Can you give an example of how this is worked out on paper?
how do you do AB * AC. If both are 3x1 matrices, how can they multiply?

8. ## Re: Converting a Vector equation to a linear equation

Vector AB = -3i -j +2k and vector AC = 3i-5j+3k
AB x AC = 7i+15j+18k and R-C = (x-4)i+(y+3)j+(z-4)k
Find (ABxAC). ( R-C)=0
Now i am sure you would be able to complete the solution