# For what values of a and b are these two vectors collinear (linear algebra)?

1. Feb 20, 2012

### BlueRope

1. The problem statement, all variables and given/known data
For what values of a and b are these two vectors collinear (linear algebra)?

t = (3a -4b +5, 5b -2a -8)
v = (-3, 4)

t and v are vectors

2. Relevant equations

3. The attempt at a solution

I'd like to know what the steps are. I don't really care about the answer.

2. Feb 20, 2012

### alanlu

t and v are collinear if t = kv for some scalar k. Expand and solve for a and b in terms of k.

3. Feb 20, 2012

### BlueRope

I was thinking of doing that, until I saw the answer, which was t = 7(a-1)(-3,4) or 7(a-1)vectorz.

4. Feb 20, 2012

### BlueRope

Basically, he wrote 6a -b -4 = 0

then he isolated b, which gives:

b = 6a -4

then he somehow came with

the answer, which is, like I said:

t = 7(a-1)(-3,4) or 7(a-1)vector z.

I have no idea what the teacher did.

5. Feb 20, 2012

### alanlu

Another way of determining vectors are collinear is to see if the dot product of one of the vectors and basis vectors of the other vector's orthogonal space evaluate to 0. In the plane, a vector v's orthogonal space has one dimension and is in fact perp v.

It appears that the equation t * perp v = 0 was solved for b here.

6. Feb 20, 2012

### BlueRope

I finally understood how he did it. However, I don't understand how it answers the question. He wanted the values of b and a, but we only got the value of k.

If the answer is 7(a-1) vector z then a GENUINE answer would be: b = 0 and a = R or any value, right?

7. Feb 20, 2012

### alanlu

I don't understand where 7(a-1) vector z is from here, but letting a = R gives b = 6R - 4. Values a, b such that b = 6a -4 should be enough to answer this question.