# Homework Help: Scalar projection of b onto a (vectors)

1. Sep 9, 2010

### TsAmE

1. The problem statement, all variables and given/known data

If a = <3,0,-1> find the vector b such that compaB = 2

2. Relevant equations

None.

3. The attempt at a solution

$$|a| =\sqrt{3^2 + 1^2} = \sqrt{10}$$

compaB = $$\frac{ a\cdot b}{|a|}$$

$$2 = \frac{3(b1) - 1(b3)}{\sqrt{10}}$$

$$2\sqrt{10} = 3(b1) - 1(b3)$$

I dont know what to do from here

2. Sep 9, 2010

### CompuChip

You said, find the vector b whose projection on a is twice as long as a itself, but of course there are infinitely many such vectors. What you have shown here is that there is that a vector of the form b = (r, s, 3r - 2√10) for any real numbers r and s satisfies compab = 2.

3. Sep 9, 2010

### TsAmE

Sorry but I dont understand.