Answer the following. a) Suppose that pi ∈ R3 vectors and wi ∈ R 3 nonzero vectors. If v1(t) = p1 + tw1 and v2(t) = p2 + tw2, are vector equations of the same line, show that w1, w2 are multiples of each other and p1 − p2 is a multiple of w1. ] b) Suppose that p1, p2, w1, w2 are vectors in R 3 with w1, w2 6= 0 and that w1, w2 are multiples of each other and that p1−p2 is a multiple of w1. Prove that v1(t) = p1+tw1 and v2(t) = p2+tw2 define the same line.
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