# Vectors and magnitudes

1. Jan 9, 2014

### negation

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

Vector A has magnitude 3 and points to the right. Vector B has magnitude 4 and points vertically upwards. Find the magnitude of vector C such that A + B + C = 0

3. The attempt at a solution

C = SQRT[4^2 + 5^2] = 6.4

2. Jan 9, 2014

### SteamKing

Staff Emeritus
Draw a picture.

3. Jan 9, 2014

### CWatters

What SteamKing said. It's not 6.4

4. Jan 9, 2014

### Staff: Mentor

Where did the "5" come from?

5. Jan 9, 2014

### NasuSama

Very good idea to draw a picture as SteamKing said.

Another approach is to express the direction of the vectors with $\hat{i}$ and $\hat{j}$ components, where $\hat{i}$ represents the x-direction of the vector and $\hat{j}$ represents the y-direction of the vector.

Here is the concrete demonstration of the vectors: if a vector points to the right, then we obtain the positive $\hat{i}$ component. If a vector points up, then we obtain the positive $\hat{j}$ component. From here, we see that if a vector points up and right, then we obtain both positive $\hat{i}$ and $\hat{j}$ components.

Remember, when combining vectors, you have to add their magnitudes component-wise as you do with variables in pre-calculus class.

Note: The combination of those two vectors don't give you the answer you want since it points up-right. You need to figure out the vector $\vec{C}$ in which $\vec{A} + \vec{B} + \vec{C} = 0$

6. Jan 9, 2014

### negation

It should be 3^2. Careless blunder

7. Jan 9, 2014

8. Jan 9, 2014

### Staff: Mentor

Your C vector has two heads. It should only have one. Which one do you judge is the correct one?
Chet

9. Jan 9, 2014

### negation

The correct one points to the left.

10. Jan 9, 2014

### NasuSama

The vector $\vec{C}$ does NOT point to the right. As I mentioned before:

The combination of those two vectors don't give you the answer you want since it points up-right. You need to figure out the vector $\vec{C}$ in which $\vec{A} + \vec{B} + \vec{C} = 0$

Good. Also, which $y$-direction is the vector $\vec{C}$ pointing at? Remember that its direction is opposite to the combination of the two vectors $\vec{A}$ and $\vec{B}$, which points up-right. The vector $\vec{C}$ does not only point to the left. It also points... (You figure out the y-direction)

11. Jan 9, 2014

### negation

It also points downwards. It is in the direction -j hat

12. Jan 9, 2014

### NasuSama

Nicely done. ;) Finally, determine the magnitude of $\vec{C}$, and you are done.

13. Jan 10, 2014

### negation

Magnitude of c = 5

14. Jan 10, 2014

yep :)