Ex 11.1, 3 - If a line has direction ratios -18, 12, -4, then - Ex 11.1

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  1. Chapter 11 Class 12 Three Dimensional Geometry
  2. Serial order wise
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Ex 11.1, 3 If a line has the direction ratios −18, 12, −4, then what are its direction cosines? If direction ratios of a line are a, b, c direction cosines are 𝑎﷮ ﷮ 𝑎﷮2﷯ + 𝑏﷮2﷯ + 𝑐﷮2﷯﷯﷯ , 𝑏﷮ ﷮ 𝑎﷮2﷯ + 𝑏﷮2﷯ + 𝑐﷮2﷯﷯﷯ , 𝑐﷮ ﷮ 𝑎﷮2﷯ + 𝑏﷮2﷯ + 𝑐﷮2﷯﷯﷯ Given, Direction ratios = − 18, 12, −4 𝑎 = − 18, b = 12, c = −4 ﷮𝑎2+𝑏2+𝑐2﷯ = ﷮ − 18﷯2+122+ −4﷯2﷯ = ﷮324+144+16﷯ = ﷮484﷯ = 22 Direction cosines = 𝑎﷮ ﷮ 𝑎﷮2﷯ + 𝑏﷮2﷯ + 𝑐﷮2﷯﷯﷯ , 𝑏﷮ ﷮ 𝑎﷮2﷯ + 𝑏﷮2﷯ + 𝑐﷮2﷯﷯﷯ , 𝑐﷮ ﷮ 𝑎﷮2﷯ + 𝑏﷮2﷯ + 𝑐﷮2﷯﷯﷯ = −18﷮22﷯ , 12﷮22﷯ , −4﷮22﷯ = −𝟗﷮𝟏𝟏﷯ , 𝟔﷮𝟏𝟏﷯ , −𝟐﷮𝟏𝟏﷯

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