3D Real Space

3D real space, referred to as ${\mathbb{R}}^3$ has many useful properties such as being used to graph bivariate functions.

In ${\mathbb{R}}^3$, the Unit vectors that are usually used, and correlate with the x, y and z directions are:

$$\hat{i}=(1,0,0)\hat{j}=(0,1,0)\hat{k}=(0,0,1)$$

Note that that hat notation (^) defines a unit vector

Any Vector in ${\mathbb{R}}^3$ can be written as a linear combination of these unit vectors:

$$\vec{v}=(v_1,v_2,v_3)=(v_1\hat{i},v_2\hat{j},v_3\hat{k})$$