JEE Main2008MathematicsThree Dimensional GeometryActual

The line passing through the points (5,1, a) and (3, b, 1) crosses the y z- plane at the point (0, 17 2 , -13 2 ) . Then

Options

Aa=2, b=8
Ba=4, b=6
Ca=6, b=4
Da=8, b=2

Correct answer

C. a=6, b=4

Step-by-step solution

Equation of line passing through (5,1, a) and (3, b, 1) is x-5 2 = y-1 1-b = z-a a-1 = If line crosses y z- plane i.e., x=0 aligned & x=2 +5=0 & =-5 / 2, aligned Since, y= (1-b)+1= 17 2 aligned & - 5 2 (1-b)+1= 17 2 & b=4 aligned Also, z= (a-1)+a=- 13 2 aligned & - 5 2 (a-1)+a=- 13 2 & a=6 aligned

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