Question

On Cartesian coordinates pdf on page 3 it states
that the x-component vector of a vector is not the magnitude of the vector (I can't seem to type formulas, vectors here so please see pdf)
http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/mathematics-the-language-of-science/cartesian-coordinates-and-vectors/MIT8_01SC_coursenotes03.pdf

It also states that the magnitude is given by (Ax^2)^1/2
now if you take a number any number and do that operation on it (x^2)^1/2 you end up with the same number.
So what difference does it make?

Answer 1

I looked for the equation (Ax^2)^1/2, but could not find it. I don't recognize that as a formula for the magnitude of a vector. Here is the formula for the magnitude of a vector in three space:
\[\text{Let v be a vector, with components } v_x,v_y,v_z,\]

\[\text{then the magnitude is given by} \sqrt{v_{x}^2+v_{y}^2+v_{z}^2}.\]

Answer 2

By the way, it seems that formulas only work for replies, so you have to post the question, then tack on the formulas later, if you want them to look pretty.

Answer 3

sorry its on page 12, I don't know how I put page 3
this is what it says:
The x-component vector \[A _{x}\] can be positive, zero, or negative. It is not the magnitude of \[A _{x}\] (with arrow on top of A, I don't know to get the arrow here) which is given by \[(A _{x}^{2})^{1/2}\].

Answer 4

Ah, ok. On that page it says: "Note the difference between the x-component \[A_{x}\] and the x-component vector \[\overrightarrow{A_{x}}\],

The second one is a full three dimensional vector with a y component that equals 0, and a z component that equals zero, and the magnitude equation I posted above reduces to the equation they gave, which is really just an absolute value equation. It takes the x component and removes the sign from it.