JEE Main2016MathematicsThree Dimensional GeometryActual

The distance of the point 1 , - 5 , 9 from the plane x - y + z = 5 measured along the line x = y = z is

Options

A10 3
B20 3
C3 10
D10 3

Correct answer

D. 10 3

Step-by-step solution

Equation of line parallel to x = y = z through 1 , - 5 ,   9 is x - 1 1 = y + 5 1 = z - 9 1 = λ If P  λ + 1 ,   λ - 5 ,   λ + 9 be point of intersection of line and plane. ⇒ λ + 1 - λ + 5 + λ + 9 = 5 ⇒ λ =   - 10 ⇒ Coordinate points are - 9 ,   - 15 ,   - 1 ⇒ Required distance = λ 1 2 + 1 2 + 1 2 = 10 3

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