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JEE Main20199 Jan 2019Evening ShiftMathematicsThree Dimensional GeometryActual

If the lines x = a y + b , z = c y + d and x = a ′ z + b ′ ,    y = c ′    z + d ′ are perpendicular, then

Options

  1. Ac c ’ + a + a ’ = 0
  2. Ba a ’ + c + c ’ = 0
  3. Cb b ’ + c c ’ + 1 = 0
  4. Da b ’ + b c ’ + 1 = 0

Correct answer

B. a a ’ + c + c ’ = 0

Step-by-step solution

Direction Ratios of the first line i ^ j ^ k ^ 1 - a 0 0 c - 1 = a   i ^ + j ^ + c k ^   Hence, Direction Ratios of the first line are a ,   1 ,   c . For Direction Ratios of the second line i ^ j ^ k ^ 1 0 - a ′ 0 1 - c ′ = a ′ i ^ + c ′ j ^ + k ^ Hence, Direction Ratios of the 2 n d line = a ′ ,   c ′ ,   1 Since, both the lines are perpendicular, a . a ′ + c ′ + c = 0

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