# Component form

1. Dec 11, 2013

### Zondrina

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

I have two questions.

1. For the three vectors shown in this diagram: http://gyazo.com/9a23c78c8a52db6dde1ca52aee9cd2f0

The relationship $\vec{A} + \vec{B} + \vec{C} = 1\hat{j}$ holds. Write $\vec{B}$ in component form and then write $\vec{B}$ as a magnitude and direction.

2. The following figure shows two vectors $\vec{A}$ and $\vec{B}$: http://gyazo.com/750754b5c6589491df5f22788e9b3281

Find a vector $\vec{C}$ such that $\vec{A} + \vec{B} + \vec{C} = 0$ and use component form to do so.

2. Relevant equations

$\vec{A} = \vec{A}_x + \vec{A}_y + \vec{A}_z = A_x \hat{i} + A_y \hat{j} + A_z \hat{k}$

3. The attempt at a solution

My work for part 1 and part 2 are displayed below:

Part 1: http://gyazo.com/9b03c43d7bbc1cb69ded51b9b0637b77

Part 2: http://gyazo.com/6fe9e06cfb189cd8ce6ab1c24811deec

Hopefully I've done these properly. If someone could help me verify it would be much appreciated.

2. Dec 12, 2013

### voko

1a. Correct, but incomplete. Use should have used the given values for the components (what you did in 1b).

1b. I agree with the magnitude. The angle, however - with respect to what is it 37 degree? Usually it is taken with respect to the x axis, but it is clearly seen from the picture that it is between 90 and 180 degrees. And the final expression you obtained does not make any sense to me at all.

2. I agree with the method. I have not checked the numbers, though.

3. Dec 12, 2013

### Zondrina

Question 1 was split into 2 parts, namely a) and b). For part a) I think I only had to write the component form down.

For part 1 b) though, I'm not sure I understand what I've done wrong. When I found the components for $\vec{A}$ and $\vec{C}$, I switched everything so it would be in the first quadrant by adding a negative sign to $C_y$ (the book I'm using wants me to do this).

When I wrote my final answer, namely $\vec{B} = 5 [-x 36.87° +y]$, I intended it to mean $36.87°$ above the negative x axis. So $-x$ is like west and $+y$ is like north.

I'm sure if 1 is okay, 2 will be fine.

4. Dec 12, 2013

### voko

I believe you were supposed to write the component form not just in symbols, but in concrete numbers.

This isn't a notation I am familiar with, but if that is what your textbook and you teachers understand, use it. If the angle is measured from the west, then it is OK.

5. Dec 12, 2013

### Zondrina

This is just some self study. I'm trying to plow through phys for scientist & engineers by Randall d. Knight since I got tired of not knowing any real physics :).

I think I'll switch back to the old NESW convention as it's probably less confusing to me and any potential readers.

Thank you for your help though. Hard to tell if you're doing something properly if there's no teacher.