Example 2 - If line has direction ratios 2, -1, -2, find cosines - Examples

  1. Chapter 11 Class 12 Three Dimensional Geometry
  2. Serial order wise
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Example, 2 If a line has direction ratios 2, – 1, – 2, determine 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 = 2, −1, −2 𝑎 = 2, b = −1, c = −2 Also, ﷮ 𝑎﷮2﷯ + 𝑏﷮2﷯ + 𝑐﷮2﷯﷯ = ﷮22 + ( − 1)2 + ( − 2)2﷯ = ﷮4 + 1 + 4﷯ = ﷮9﷯ = 3 Direction cosines = 𝑎﷮ ﷮ 𝑎﷮2﷯ + 𝑏﷮2﷯ + 𝑐﷮2﷯﷯﷯ , 𝑏﷮ ﷮ 𝑎﷮2﷯ + 𝑏﷮2﷯ + 𝑐﷮2﷯﷯﷯ , 𝑐﷮ ﷮ 𝑎﷮2﷯ + 𝑏﷮2﷯ + 𝑐﷮2﷯﷯﷯ = 𝟐﷮𝟑﷯ , −𝟏﷮𝟑﷯ , −𝟐﷮𝟑﷯

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