What is # || < -4 , 8 , 6 > || #?
This operation is known as the magnitude. It represents how 'long' the vector is. You can imagine this vector starts from the origin and goes -4 in the x, 8 in the y and 6 in the z direction. Therefore, the length of this vector is
This might sound confusing, but take a cuboid of width, length and height: x, y and z (respectively). It is trivial to prove that using Pythagoras that the length from the bottom left hand corner to the top right hand corner is
Continue reading for a full proof of the above formula using the cuboid idea:
(Diagram at bottom):
So because of our first rule,