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Let's put the ball back on the ground, as we Brazilians used to say:
Here we have the representation of a rocket, or a spacecraft pointing toward the sky. 
First in 3D, then in  two-dimentions (2D), by coupling XY  vectors together.
29_foguete.png

Adding the fourth dimension, the problem gains a more proper formulation for the huge distances of the outer space. Curiously, since time supposedly does not move backwards, we need a slightly different Pythagorean Theorem in order calculate what is necessary to bring our astronaut back on earth.

Mathematical problems have no limit of dimensions. The same applies for the null space representation. 
30_foguete.png

Beta μ

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