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JEE Main20205 Sep 2020Morning ShiftMathematicsThree Dimensional GeometryActual

If ( a , b , c ) is the image of the point ( 1 , 2 , - 3 ) in the line, x + 1 2 = y - 3 - 2 = z - 1 , then a + b + c is equal to:

Options

  1. A2
  2. B- 1
  3. C3
  4. D1

Correct answer

A. 2

Step-by-step solution

R ( - 1 + 2 r , 3 - 2 r , - r ) d r ' s   o f   P R   a r e   ( 2 - 2   r , - 1 + 2   r , - 3 + r ) Then, 2 ( 2 - 2   r ) + 2 ( 1 - 2   r ) + 1 ( 3 - r ) = 0 9 - 9 r = 0   ⇒   r = 1 R ( 1 , 1 , - 1 ) then a + 1 = 2   , b + 2 = 2   ,   c - 3 = - 2 i.e., a = 1 , b = 0 ,   c = 1 ∴    a + b + c = 2

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