Ex 11.2, 3
Last updated at Dec. 8, 2016 by Teachoo
Transcript
Ex 11.2, 3 Show that the line through the points (4, 7, 8), (2, 3, 4) is parallel to the line through the points (โ1, โ2, 1), (1, 2, 5). Two lines having direction ratios ๐1, b1, c1 and ๐2, b2, c2 are parallel if ๐๐๏ทฎ๐๐๏ทฏ = ๐๐๏ทฎ๐๐๏ทฏ = ๐๐๏ทฎ๐๐๏ทฏ 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) Now, ๐1๏ทฎ๐2๏ทฏ = โ2๏ทฎ2๏ทฏ = โ1, ๐1๏ทฎ๐2๏ทฏ = โ4๏ทฎ4๏ทฏ = โ1 ๐1๏ทฎ๐2๏ทฏ = โ4๏ทฎ4๏ทฏ = โ1 Since ๐1๏ทฎ๐2๏ทฏ = ๐1๏ทฎ๐2๏ทฏ = ๐1๏ทฎ๐2๏ทฏ = โ1, Therefore, the given lines are parallel.
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