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Vectors.md

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Vector equation proof

taking lambda as L and Miu as M
  • Proof
let L  != 0
if so
	a = -(M/L)b <---- this is in the form of a = kb

this format means a is parallel to b (a // b)
But by definition a and b are non prallel, therefore this is impossible
So L has to be 0

if L = 0
	La + Mb = 0
	0*a + Mb = 0
	Mb = 0

This means either (M = 0) or (b = 0)
But by definition  a and b are non zero, therefore  (b = 0) is impossible
So M has to be 0

So now let, L = 0 and M = 0 

	La + Mb = 0 
	0 + 0 = 0

Therefor La + Mb = 0 only if (L = 0) and (M = 0)