# Vectors Question

1. Sep 28, 2009

### Gattz

If you are given vector a = axi + ayj + azk and you want to find the magnitude of a, then would you just do the square root of ax2 + ay2? If so, then what about az? What is azk actually? I'm a little unclear about it being related to a.

2. Sep 28, 2009

### Delphi51

You would do the square root of ax2 + ay2 + ay2.
Sorry, I don't know how to make superscripts. Too bad they don't copy.

3. Sep 29, 2009

### Gattz

You mean az for the last one?

And to do superscripts, just put "[.SUP] [/SUP.]" without the quotations and periods (caps don't matter). And it's for subscripts.

4. Sep 29, 2009

### Delphi51

Yes az, and thanks for the tip.

5. Sep 29, 2009

### Hannisch

Just a quick explanation for that azk term, if you still are unclear about it.

k adds another dimension to the vector. When a vector is only in i,j it's 2D and i,j,k is 3D. See it as drawing it in a xyz-coordinate system instead of a xy one. And as was mentioned earlier, it changes things a little bit when it comes to the magnitude. You wouldn't just do the √(ax2 + ay2), because then you wouldn't take the third dimension into consideration. From there it's not too big of a leap to √(ax2 + ay2 + az2).

You can prove it using Pythagoras' theroem. If you draw a 3D vector in a coordinate system you can figure it out. It can be a bit tricky to see, but it's not impossible.

6. Sep 29, 2009

### Gattz

7. Sep 29, 2009

### Delphi51

You could do it that way and you'll get the same answer.
It would be interesting to prove that . . .

8. Sep 29, 2009

### Gattz

Actually I just realized that the square root of az2 + ay2 is the hypothesis. So I guess it makes sense.