# Dot product question

1. Jan 27, 2009

### Random-Hero-

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

I'm really at a loss here, if anyone could help me out I'd really appreciate it.

Given 'a' and 'b' unit vectors,

if |a+b| = root3, determine (2a-5b)dot(b+3a)

2. Jan 28, 2009

### Staff: Mentor

|a + b|^2 = (a + b)$$\bullet$$(a + b)
and |a + b| = sqrt(3) ==> |a + b|^2 = 3

Now, use the fact that the dot product is associative, distributive, and commutative and the two equations above to see if you can evaluate (2a - 5b) )$$\bullet$$ (b + 3a).

3. Jan 28, 2009

### Random-Hero-

well I end up getting 13ab + 6a^2 - 5b^2

I just can't seem to figure out how to get there :s

4. Jan 28, 2009

### Staff: Mentor

Work with (a + b) $\cdot$ (a + b) = 3. You also know that a and b are unit vectors, which means that a $\cdot$ a = 1 and b $\cdot$ b = 1.

5. Jan 28, 2009

### Random-Hero-

Would I do like

(a+b)dot(a+b)=3

1 + 2ab + 1 = 3

ab = 1/2

then sub 1/2 into the ab and then get 6.5 + 6a^2 - 5b^2 and solve from there?

6. Jan 28, 2009

### Staff: Mentor

Sort of, except that what you show as 6a^2 and -5b^2 is really 6a$\cdot$ a and -5b$\cdot$ b.