A line passing through the origin is perpendicular to the lines l_1: (3+t) i +…

MATHEMATICS · Single correct · CBSE · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

A line ll passing through the origin is perpendicular to the lines l1:(3+t)i^+(−1+2t)j^+(4+2t)k^,−∞<t<∞l_1: (3+t)\hat{i} + (-1+2t)\hat{j} + (4+2t)\hat{k}, -\infty < t < \infty l2:(3+2s)i^+(3+2s)j^+(2+s)k^,−∞<s<∞l_2: (3+2s)\hat{i} + (3+2s)\hat{j} + (2+s)\hat{k}, -\infty < s < \infty Find the coordinate(s) of the point(s) on l2l_2 at a distance of 17\sqrt{17} from the point of intersection of ll and l1l_1. (1) (73,73,53)\left(\frac{7}{3}, \frac{7}{3}, \frac{5}{3}\right) (2) (−1,−1,0)(-1, -1, 0) (3) (1,1,1)(1, 1, 1) (4) (79,79,89)\left(\frac{7}{9}, \frac{7}{9}, \frac{8}{9}\right)

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