Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, -1), (4, 3, -1)

Answer

The direction ratios of the `1^st` line are 2-0, 1-0, 1-0 i.e., 2, 1, 1
the direction ratios of the `2^nd` line are 4-3, 3-5, 1-+1 i.e., 1, -2, 0 Since `2xx1+1xx-2+1xx0 = 2-2+2 = 0`, the two lines are perpendicular