Vectors - how to 'show' additive and multiplicative properties

Hi, looking back at some vector stuff from back in my alevel days, and forgotten how to go about 'showing' results. So say vectors u, v, z are of the same order and c,d are constants, how would I prove the basic

U+v = v + u and (c+d)(u + v)

Thanks

Posted from TSR Mobile

Reply 1

rayquaza17

17

https://www.youtube.com/watch?v=FahFOixgZBU

Reply 2

atsruser

11

Original post by BackToMathsAgain

Hi, looking back at some vector stuff from back in my alevel days, and forgotten how to go about 'showing' results. So say vectors u, v, z are of the same order and c,d are constants, how would I prove the basic

U+v = v + u and (c+d)(u + v)

For the additive property that you're trying to prove (commutativity), it depends on how you want to prove it. You can do it graphically via the properties of a parallelogram, or algebraically, coordinate-wise, where it's trivial since addition of real-valued coordinates is commutative.

It's not clear what multiplicative properties you want to prove, since you can't multiply vectors as you seem to be doing. Are you referring to the dot and cross products?

Reply 3

brianeverit

9

Original post by BackToMathsAgain

Hi, looking back at some vector stuff from back in my alevel days, and forgotten how to go about 'showing' results. So say vectors u, v, z are of the same order and c,d are constants, how would I prove the basic

U+v = v + u and (c+d)(u + v)

Thanks

Posted from TSR Mobile

Draw diagrams.

Reply 4

BackToMathsAgain

OP

1

Original post by rayquaza17

https://www.youtube.com/watch?v=FahFOixgZBU

Thanks very much

Reply 5

simon0

13