# Find unit vector and cross product

1. Aug 9, 2007

### Edwardo_Elric

1. The problem statement, all variables and given/known data
Given the two vectors written in component-unit vector form below:
$$D = 3\hat{i} - \hat{j}$$
$$E = 2\hat{i} + 4\hat{j}$$
a.) Find the unit vector in the same direction as D
b.) Find the cross product of D x E
c.) Write the vector D in magnitude direction form

2. Relevant equations

3. The attempt at a solution
a.)
$$\hat{u} = \frac{\vec{D}}{D}$$
$$\hat{u} = \frac{3\hat{i}}{10} - \frac{\hat{j}}{10}$$

b.) Cz = DxEy - DyEx
Cz = [3][4] - [-1][2]
= 12 + 2
= 14

c.) D = sqrt(3^2 + 1)
= 3.2
theta = tan^-1(1/-3)
= 18.4
3.2.... 18.4 degrees S of W

2. Aug 9, 2007

### learningphysics

The denominators are wrong.

Yes, that's correct. I'd write the final answer as $$14\hat{k}$$

The direction isn't right.

3. Aug 9, 2007

### Edwardo_Elric

a.) $$\hat{u} = \frac{10}{3\hat{i}} - \frac{10}{\hat{j}}$$

c.) D = 3.2, 18.4 S of W
?

4. Aug 9, 2007

### learningphysics

No, what you had before was right except that you needed sqrt(10) instead of 10 in the denominator.

I get the direction as 18.4 S of E

5. Aug 9, 2007

### Edwardo_Elric

oh yeah i thot west is to the right
thanks