# Find the magnitude and direction of each vector

1. Oct 25, 2009

### joemama69

1. The problem statement, all variables and given/known data
2. You are given three vectors: A = (6.0i— 8.0j) units B = (-8.0i + 3.0j) units and C = (26.0i + 19.0j) units.

a) Find the magnitude and direction of each vector.

b) Find the resultant of A + B, A - B and A + B - C.

c) It is know that aA + bB + C = 0. Find the values of a and b that satisfy this vector equation.

2. Relevant equations

3. The attempt at a solution

For part A, what does it mean to find the direction of each vector. do they want the angle

2. Oct 25, 2009

### emyt

Re: Vectors

yes they do

3. Oct 25, 2009

### flatmaster

Re: Vectors

I assume they want the angle of the vector. By convention, the angle is measured counter-clockwise from the positive x axis. Think of how you drew the unit circle in trigonometry.

For B, you simply add components.

Part C, you Have what appears to be one equation and two unknowns. However, it's a vector equation, which in your case is actually two equations. There's one for your x components and one for your y components.

4. Oct 27, 2009

### joemama69

Re: Vectors

so i would do

a(6.0i— 8.0j) +b(-8.0i + 3.0j) + (26.0i + 19.0j) = 0

6a - 8b + 26 = 0

-8a + 3b + 19 = 0 and just solve this system

5. Oct 27, 2009

Re: Vectors

Yes. Correct