Question

\[\newcommand\ve[1]{\vec{\boldsymbol #1}} % vector
\newcommand\uv[1]{\hat{\boldsymbol #1}} % unit vector
\begin{equation*}\ve A=\begin{bmatrix}a_1\\a_2\\a_3\end{bmatrix}=\langle a_1,a_2,a_3\rangle\\
\end{equation*}\]?

Answer 1

If the column matrix is the same as the vector?

Answer 2

maybe

Answer 3

i hope so

Answer 4

I don't understand the question (if this is a question) :(

Answer 5

well i'm trying to understand the different notations,,

Answer 6

It depends on the situation. In one case you can use different notations for the vector and in another - you cant.

Answer 7

can you explain why that is so
?

Answer 8

Yes, I can. Do you know anything about matrix multiplication?

Answer 9

yeah,

Answer 10

So I show a case, when the row notation and the column notation should not be confused.
Lets take two vectors:
\(\vec{a}=\left(\begin{matrix}1\\2\end{matrix}\right)\) and \(\vec{b}=(3,4)\).
And now multiply \(\vec{a}\) on \(\vec{b}\), and then \(\vec{b}\) on \(\vec{a}\):
\(\vec{a}\vec{b}=\left(\begin{matrix}1\\2\end{matrix}\right)(3,4)=\left(\begin{matrix}3&4\\6&8\end{matrix}\right)\)
\(\vec{b}\vec{a}=(3,4)\left(\begin{matrix}1\\2\end{matrix}\right)=3\cdot1+4\cdot2=11\)
If we confuse the rows and the columns we will have the wrong result, because it is important to know where is the column and where is the row.

But in other case, when we say about a vector in general, without multiplication, it is not so important to know if it is a row or a column.

Answer 11

do the different vectors fit the same cartesian plane?

Answer 12

2D vectors can represent the points of the cartesian plane. So the different vectors represent different points. And they fit this plane.

Answer 13

Do you have a concrete example, so I can help you?

Answer 14

or should one of those be on the z axis?

Answer 15

It is ok. Why do you think any of those must be on z-axis?
One more question: how did you draw this pic?

Answer 16

http://openstudy.com/study#/updates/50f4096be4b0694eaccfaa5d

Answer 17

Oh. I thought about it, but it is too long to draw pics in TikZ. Or you have good skills?

Answer 18

i just made my first 3d template on ti\(k\)z today

Answer 19

i suppose i think the different vectors look different, so they must be orthogonal somehow

Answer 20

* i mean the notation is different

Answer 21

No. Different vectors on the plane are the vectors, that has different components. The notation doesn't play any role.

Answer 22

ok so then, the operation of multiplying the vectors somehow chooses that the first vector to be a row vector for dot product, right?

Answer 23

Scalar product of the vectors is just a particular case of the general multplication of the matrices.

Answer 24

can you graph a matrix?

Answer 25

You have to know what a matrix interprete. It is a table of numbers.
My answer is No.

Answer 26

not even a 2x2 matrix?

Answer 27

No. How do you think, what does this matrix will show on the plane?
A components of the vectors can be read as the point, but what is a matrix?

Answer 28

since you written an arrow on top of the A, I assume it is a vector. So the vector is 3 dimensional in R^3. Let the a's equal x, y, and z standing for its components. The second is written in column form and the last one is written in row form.

I hope this answers your question. They are both equal but written differently notation wise.