U=(3, 3 , 3) and column vector.

[DUET]

If u=(3, 3 , 3) is a vector in R³ then we can draw the vector in a three dimensional space.(3=x coordinate, 3= y coordinate, 3= z coordinate.)

if x = \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_m \end{bmatrix} is a column vector in R^m then how can we draw it?
In addition we call X = \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_m \end{bmatrix} column vector. My question is what is the name of u=(3, 3 , 3) vector?

 

[mfb]

There is no single, general way to draw a vector of an n-dimensional space on paper if n>3. There might be some interesting methods for specific applications, but you always have to ignore some components, or use other tools like color codes or whatever.

Row vector.

 

[DUET]

I think u=(3, 3 , 3)^T is a column vector, three dimensional. How can I draw it now?

 

[HallsofIvy]

Yes, it is obviously "three dimensional". Being a "column" vector as opposed to a "row" vector is irrelevant here. You draw such a vector, in two dimensions, by projecting the three dimensional vector onto the two dimensional surface. How you do that depends upon what kind of projection you want to use and, most importantly, from which direction you are looking at the vector.

 

[blue_raver22]

The vector u=(3, 3, 3) is a specific instance of a column vector, as it follows the same format of a column vector with three elements. It could also be referred to as a three-dimensional vector, as it has three components in a three-dimensional space. However, the name of a vector is not as important as its representation and understanding of its properties and characteristics. In this case, u=(3, 3, 3) represents a vector in R3 with equal components in each dimension, and it can be drawn as a point in a three-dimensional space.