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in Vector algebra by (36.3k points)

Let A(t) = f1(t)i + f2(t)j and B(t) = g1(t)i + g2(t)j, t ∈ [0, 1], where f1, f2, g1, g2 are continuous functions. If A(t) and B(t) are non-zero vectors for all t and A(0) = 2i + 3j, A(1) = 6i + 2j, B(0) = 3i + 2j, B(1) = 2i + 6j, show that A(t), B(t) are parallel for some t.

1 Answer

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Best answer

A(t) is parallel to B(t) for some t in [0, 1]

= 6.6 – 2.2 = 32 > 0

since h is a continuous function and h(0)h(1) < 0

Then there is some t in [0, 1] for which h(1) = 0

Thus, A(t) is parallel to B(t) for this t.

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