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Last updated at Dec. 8, 2016 by Teachoo
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Ex 11.2, 1 Show that the three lines with direction cosines 1213, − 313, − 413 ; 413, 1213, 313 ; 313, − 413, 1213 are mutually perpendicular. Two lines with direction cosines 𝑙1, 𝑚1 , 𝑛1 & 𝑙2, 𝑚2 , 𝑛2 are perpendicular to each other if 𝒍𝟏 𝒍𝟐 + 𝒎𝟏 𝒎𝟐 + 𝒏𝟏 𝒏𝟐 = 0 𝑙1 𝑙2 + 𝑚1 𝑚2 + 𝑛1 𝑛2 = 1213 × 413 + −313 × 1213 + −413 × 313 = 48169 + −36169 + −12169 = 48 − 36 −12169 = 48 − 48169 = 0 ∴ 𝑙1 𝑙2 + 𝑚1 𝑚2 + 𝑛1 𝑛2 = 0 Hence, the two lines are perpendicular. Now, 𝑙2 𝑙3 + 𝑚2 𝑚3 + 𝑛2 𝑛3 = 413× 313 + 1213 × − 413 + 313 × 1213 = 12169 + − 48169 + 36169 = 12 − 48 + 36169 = 48 − 48169 = 0 ∴ 𝑙2 𝑙3 + 𝑚2 𝑚3 + 𝑛2 𝑛3 = 0 Hence, the two lines are perpendicular.
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