the equationof a plane is `2x-y-3z=5 and A(1,1,1),B(2,1,-3),C(1,-2,-2) and D(-3,1,2)` are four points. Which of the following line segments are intersects by the plane? (A) AD (B) AB (C) AC (D) BC

Let (1,2,0) , B(2,0,4) , C (1,1,2) & D(0,1,3) be four points in space then the length of projection of line segment AB on the line C D is

Show that the four points A(1,-1,1), B(2,3,1),C(1,2,3) and D(0,-2,3) are coplanar. Find the equation of the plane containing them.

Let the equations of two planes be P_1: 2x-y+z=2 and P_2: x+2y-z=3 Equation of the plane which passes through the point (-1,3,2) and is perpendicular to each of the plane P_1 and P_2 is (A) x-3y-5z+20=0 (B) x+3y+5z-18=0 (C) x-3y-5z=0 (D) x+3y-5z=0

Consider a plane x+2y+3z=15 and a line (x-1)/(2)=(y+1)/(3)=(z-2)/(4) then find the distance of origin from point of intersection of line and plane.

If A(4, 2, 1), B(2, 1, 0), C(3, 1, -1), D(1, -1, 2) , then the volume of the paralleloP1ped with segments AB, AC, AD as a concurrent edges is

Consider a plane P:2x+y-z=5 , a line L:(x-3)/(2)=(y+1)/(-3)=(z-2)/(-1) and a point A(3, -4,1) . If the line L intersects plane P at B and the xy plane at C, then the area (in sq. units) of DeltaABC is

Find the ratio in which the line segment joining the points (2,-1,3) and (-1,2,1) is divided by the plane x+y+z=5 .

A,B and C are points in the xy plane such that A(1,2);B(5,6) and AC=3BC .Then

A plane bisects the line segment joining (-3,-3,4) and (3,7,6) and also perpendicular to this line,then the point lies on the plane can be (a) (1,-2,3) (b) (1,2,2) (c) (3,-5,2) (d) (3,-1,0)