Let and be two lines in space

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Let r=a+λlr = a + \lambda l and r=b+μmr = b + \mu m be two lines in space, where a=5i+j+2ka = 5i + j + 2k , b=−i+7j+8kb = -i + 7j + 8k , l=−4i+j−kl = -4i + j - k , and m=2i−5j−7km = 2i - 5j - 7k , then the position vector of a point which lies on both of these lines, is (1) i+2j+ki + 2j + k (2) 2i+j+k2i + j + k (3) i+j+2ki + j + 2k (4) non-existent as the lines are skew

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