# Vectors problem

1. Jun 5, 2012

### LocalStudent

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

The following are all vectors:
A = <2, 1, 1>
B = <1, -2, 2>
C = <3, -4, 2>

Find the projection of (A + C) in the direction of B

2. Relevant equations

Dot product?

3. The attempt at a solution

I was not sure what the meant in this question.

I added A and C and I got (A+C) = <5, -3, 3>

Then I did (A+C)dot(B) and I got that equal to 16

I was also thinking of dotting (A+C) with the unit vector of B?

2. Jun 5, 2012

### Infinitum

Dot product is exactly what you want to do.

$$\vec{X}\cdot\vec{Y} = |X|\cdot|Y|cos\theta$$

You have the dot product, |X|, |Y|, and you need cosine of the angle

3. Jun 5, 2012

### LocalStudent

So is the question basically asking "What is the angle between (A+C) and B?"

4. Jun 5, 2012

### Infinitum

No, it is asking you for the projection(component) of A+C on B. What is the component of a vector X on another vector Y when the angle between them is θ??

5. Jun 5, 2012

### LocalStudent

ok, I see. Thanks for the help.