For every real number

MATHEMATICS · Multi-part · CBSE · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

For every real number tt, define the points P(t, 2t−1, 3t+2)P(t,\,2t-1,\,3t+2), Q(t+1, 2t+1, 3t+5)Q(t+1,\,2t+1,\,3t+5) and R(t−2, 2t−5, 3t−4)R(t-2,\,2t-5,\,3t-4). (a) Prove that PP, QQ and RR are collinear for every real tt. (b) Find the vector equation of the straight line containing the three points. (c) For t=2t=2, determine the ratio in which QQ divides PRPR, specifying the nature of the division.

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