# Thread: Vector/Equation problem

1. ## Vector/Equation problem

Three collinear vectors, a, b, and c, are such that a=(2/3)b and a=1/2c.

Determine integer values for m and n such that mc +nb = 0. How many values are possible for m and n to make this statement true?

P.S. Variables "a," "b," c," and "0" are vectors.

I'm a little lost on how you'd solve this.

2. Originally Posted by IanCarney
Three collinear vectors, a, b, and c, are such that a=(2/3)b and a=1/2c.
Determine integer values for m and n such that mc +nb = 0. How many values are possible for m and n to make this statement true?
Can you show that does in fact work?

3. Originally Posted by Plato
Can you show that does in fact work?
Like this?

b=(3/2)a and c=2a

2m+3/2n=0

4m+3n=0

The answer in the book is: Answers may vary. For example: m=4, n=-3, infinitely many

4. Originally Posted by IanCarney
The answer in the book is: Answers may vary. For example: m=4, n=-3, infinitely many
That is correct. Any value of m gives a value for n.

### three collinear vectors a b and c are such that a 2 3b and a 1 2c

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