Let v1 , v2 R3 such that v1 and v2 are orthogonal and are both unit vectors. (a) Prove that {v1,v2} is linearly independent. (b) Let P be the plane…

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4. Let ⃗v1 ,⃗ v2 ∈ R3 such that ⃗v1 and ⃗v2 are orthogonal and are both unit vectors.

(a) Prove that {⃗v1,⃗v2} is linearly independent. (b) Let P be the plane in R3 defined by P = Span{⃗v1,⃗v2}. Prove that for any ⃗x ∈ R3 we have

projP (⃗x) = (⃗x · ⃗v1)⃗v1 + (⃗x · ⃗v2)⃗v2

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