Here's the question you clicked on:
UnkleRhaukus
\[\newcommand\ve[1]{\vec{\boldsymbol #1}} % vector \newcommand\uv[1]{\hat{\boldsymbol #1}} % unit vector \begin{equation*}\ve A=\begin{bmatrix}a_1\\a_2\\a_3\end{bmatrix}=\langle a_1,a_2,a_3\rangle\\ \end{equation*}\]?
If the column matrix is the same as the vector?
I don't understand the question (if this is a question) :(
well i'm trying to understand the different notations,,
It depends on the situation. In one case you can use different notations for the vector and in another - you cant.
can you explain why that is so ?
Yes, I can. Do you know anything about matrix multiplication?
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.
do the different vectors fit the same cartesian plane?
2D vectors can represent the points of the cartesian plane. So the different vectors represent different points. And they fit this plane.
Do you have a concrete example, so I can help you?
or should one of those be on the z axis?
It is ok. Why do you think any of those must be on z-axis? One more question: how did you draw this pic?
http://openstudy.com/study#/updates/50f4096be4b0694eaccfaa5d
Oh. I thought about it, but it is too long to draw pics in TikZ. Or you have good skills?
i just made my first 3d template on ti\(k\)z today
i suppose i think the different vectors look different, so they must be orthogonal somehow
* i mean the notation is different
No. Different vectors on the plane are the vectors, that has different components. The notation doesn't play any role.
ok so then, the operation of multiplying the vectors somehow chooses that the first vector to be a row vector for dot product, right?
Scalar product of the vectors is just a particular case of the general multplication of the matrices.
can you graph a matrix?
You have to know what a matrix interprete. It is a table of numbers. My answer is No.
not even a 2x2 matrix?
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?
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.