What is ||<−4,8,6>||?

1 Answer
LewisCroney
May 17, 2016

2√29

Explanation:

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 √(−4)2+82+62. Which simplifies down to √116 and then to 2√29

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 √x2+y2+z2. And now with that knowledge, that line represents this vector within that space. And so that's the magnitude.

Continue reading for a full proof of the above formula using the cuboid idea:

(Diagram at bottom):
Consider that x2+y2=a2, by Pythagoras.
And a2+z2=d2.
So because of our first rule, x2+y2+z2=d2
So finally, d=√x2+y2+z2.

enter image source here

Related questions
See all questions in Vector Operations
Impact of this question
1956 views around the world
You can reuse this answer
Creative Commons License