JEE Main2005MathematicsThree Dimensional GeometryActual

The distance between the line r =2 i -2 j +3 k + ( i - j +4 k ) and the plane r ( i +5 j + k )=5 is

Options

A10 9
B10 3 3
C3 10
D10 3

Correct answer

B. 10 3 3

Step-by-step solution

Distance between the line r =2 i -2 j +3 k + ( i - j +4 k ) and the plane r ( i +5 j + k )=5 is equation of plane is x+5 y+z=5 Distance of line from this plane = perpendicular distance of point (2,-2,3) from the plane i.e. | 2-10+3-5 1+5^2+1 |= 10 3 3 .

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