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Last updated at Feb. 1, 2020 by Teachoo
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Misc 1 Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, โ 1), (4, 3, โ 1).Two lines having direction ratios ๐1, ๐1 , ๐1 and ๐2, ๐2, ๐2 are Perpendicular to each other if ๐1 ๐2 + ๐1 ๐2 + ๐1 ๐2 = 0 Also, a line passing through (x1, y1, z1) and (x2, y2, z2) has the direction ratios (x2 โ x1), (y2 โ y1), (z2 โ z1) A (0, 0, 0) B (2, 1, 1) Direction ratios : (2 โ 0), (1 โ 0), (1 โ 0) = 2, 1, 1 โด ๐1 = 2, ๐1 = 1, ๐1 = 1 C (3, 5, โ1) D (4, 3, โ1) Direction ratios: (4 โ 3), (3 โ 5), ( โ1 + 1) = 1, โ2, 0 โด ๐2 = 1, ๐2 = โ2, ๐2 = 0 Now, ๐1 ๐2 + ๐1 ๐2 + ๐1 ๐2 = (2 ร 1) + (1 ร โ2) + (1 ร 0) = 2 + (โ2) + 0 = 2 โ 2 = 0 Therefore, the given two lines are perpendicular
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