Some undefined Terms - Point;Line and Plane

Some Terms

Give the correct matching of the statements of column A and Column B .Point are collinear Line is completely known Two lines in a plane Relations between points and lines in a plane collinear points A plane extends Indefinite number of lines Point,line and plane are

The number of lines that can be formed from 12 points in a plane of which 6 points lie on a line is

If z is a complex number different form i/3 then locus of z if |(3z)/(3z-i)|=1 is (A) a straightline paralel to x axis (B) a straight line having slope undefined (C) as straight line having slope 0 (D) a straight line passing through the point (2,1/6)

Distance between lines, point and plane

Find the vector equationof the line passing through the point (3,1,2) and perpendicular to the plane vecr.(2hati-hatj+hatk)=4 . Find also the point of intersection of this line and the plane.

Find the ratio in which the plane 2x-3y+z=8 divides the line segment joining the points A(3, -2,1) and B(1, 4, -3). Also find the point of intersection of the line and the plane.

A variable line passing through the point P(0, 0, 2) always makes angle 60^(@) with z-axis, intersects the plane x+y+z=1 . Find the locus of point of intersection of the line and the plane.