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**twilightmage13** Show that three vectors a, b, c lie on the same plane through the origin, if and only if there are three scalars α, β, γ not all zero such that αa + βb + γc = 0.

I believe in order to prove this, I need to show:

(1) If a, b, c lie on the same plane through the origin, then there are three scalars α, β, γ not all zero such that αa + βb + γc = 0 (i.e. the vectors are linearly dependent?).

(2) If there are three scalars α, β, γ not all zero such that αa + βb + γc = 0 (i.e. the vectors are linearly dependent?), then a, b, c lie on the same plane through the origin.

I've made an attempt at proving (1) by trying to prove the contrapositive "if there DOES NOT EXIST three scalars α, β, γ not all zero such that αa + βb + γc = 0 (i.e. the vectors are linearly independent?), then three vectors a, b, c DO NOT lie on the same plane through the origin" but I'm not sure if this is the right approach. I'm also unsure how to proceed from here.