# 3 dimensional vector

1. Oct 23, 2007

### rphmy

V1–V2 +V3 = 2i+2j+3k, V1– 2V2-2V3 = -5i+7j+8k, and V1+V2+V3 = 4i-2j-k

a) Find V1,V2, and V3

b) Find V=V1+V3 in terms of its components. What is the magnitude and direction of V?

All I know is that they are three dimensional vectors.

Any help will be much appreciated

2. Oct 23, 2007

### odie5533

$$\vec{V}_{1} = 2\hat{i} + 2\hat{j} + 3\hat{k} + \vec{V}_{2} - \vec{V}_{3}$$
Using substitution you should be able to solve for the 3 vectors.

3. Oct 23, 2007

### HallsofIvy

Staff Emeritus
Essentially, you are talking about solving three linear equations for the three unknowns,
V1, V2, and V3. odie5533's suggestion is good. It also appears that if you multiply the equation V1–V2 +V3 = 2i+2j+3k by 2 to get 2V1–2V2 +2V3 = 4i+4j+6k,and add that to the first equation, V1– 2V2-2V3 = -5i+7j+8k, you eliminate V3 from the equations. Treat it exactly like solving simultaneous.