Ex 11.2, 3 - Show line (4, 7, 8), (2, 3, 4) is parallel to - Angle between two lines - Direction ratios or cosines

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  1. Chapter 11 Class 12 Three Dimensional Geometry
  2. Serial order wise
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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 (โ€“1, โ€“2, 1), (1, 2, 5). Two lines having direction ratios ๐‘Ž1, b1, c1 and ๐‘Ž2, b2, c2 are parallel if ๐’‚๐Ÿ๏ทฎ๐’‚๐Ÿ๏ทฏ = ๐’ƒ๐Ÿ๏ทฎ๐’ƒ๐Ÿ๏ทฏ = ๐’„๐Ÿ๏ทฎ๐’„๐Ÿ๏ทฏ Also, a line passing through (x1, y1, z1) and (x2, y2, z2) has the direction ratios (x2 โˆ’ x1), (y2 โˆ’ y1), (z2 โˆ’ z1) Now, ๐‘Ž1๏ทฎ๐‘Ž2๏ทฏ = โˆ’2๏ทฎ2๏ทฏ = โ€“1, ๐‘1๏ทฎ๐‘2๏ทฏ = โˆ’4๏ทฎ4๏ทฏ = โ€“1 ๐‘1๏ทฎ๐‘2๏ทฏ = โˆ’4๏ทฎ4๏ทฏ = โ€“1 Since ๐‘Ž1๏ทฎ๐‘Ž2๏ทฏ = ๐‘1๏ทฎ๐‘2๏ทฏ = ๐‘1๏ทฎ๐‘2๏ทฏ = โˆ’1, Therefore, the given lines are parallel.

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