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AP EAMCET202023 Sep 2020Morning ShiftMathematicsThree Dimensional GeometryActual

If a 1 , b 1 , c 1 , a 2 , b 2 , c 2 are the direction cosines of two lines making an angle θ with each other, then cos θ =

Options

  1. Aa 1 a 2 + b 1 b 2 + c 1 c 2
  2. Ba 1 a 2 + b 1 b 2 + c 1 c 2
  3. Ca 1 a 2 + b 1 b 2 + c 1 c 2 / a 1 2 a 2 2 + b 1 2 b 2 2 + c 1 2 c 2 2
  4. D4 3

Correct answer

B. a 1 a 2 + b 1 b 2 + c 1 c 2

Step-by-step solution

Since a 1 , b 1 , c 1 , a 2 , b 2 , c 2 are direction cosines of the two lines. ⇒ a 1 2 + b 1 2 + c 1 2 = 1   &   a 2 2 + b 2 2 + c 2 2 = 1 Now, cos θ = ( a 1 a 2 + b 1 b 2 + c 1 c 2 ) a 1 2 + b 1 2 + c 1 2 a 2 2 + b 2 2 + c 2 2 ⇒ cos θ = ( a 1 a 2 + b 1 b 2 + c 1 c 2 ) .

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