Consider the points O(0,0),A(0,1), and B(1,1) in the x-y plane. Suppose that points C(x,1)andD(1,y) are chosen such that 0 < x < 1. And such that O,C,andD are collinear. Let the sum of the area of triangles OAC and BCD be denoted by S. Then which of the following is/are correct?.

Consider the points O(0,0), A(0,1) , and B(1,1) in the x-y plane. Suppose that points C(x,1) and D(1,y) are chosen such that 0ltxlt1 . And such that O,C, and D are collinear. Let the sum of the area of triangles OAC and BCD be denoted by S. Then which of the following is/are correct?. (a) Minimum value of S is irrational lying in ( 1 / 3 , 1 / 2 ) (b) Minimum value of S is irrational in ( 2 / 3 , 1 ) . (c) The value of x for the minimum value of S lies in ( 2 / 3 , 1 ) . (d) The value of x for the minimum values of S lies in ( 1 / 3 , 1 / 2 ) .

Find the image of the point O(0,0,0) in the plane 3x+4y-6z+1=0

Show that the points (a,0),(0,b) and (x,y) are collinear if x/a+y/b=1.

If each of the points (x_1,4),(-2,y_1) lies on the line joining the points (2,-1)a n d(5,-3) , then the point P(x_1,y_1) lies on the line. (a) 6(x+y)-25=0 (b) 2x+6y+1=0 (c) 2x+3y-6=0 (d) 6(x+y)+25=0

If each of the points (x_1,4),(-2,y_1) lies on the line joining the points (2,-1)a n d(5,-3) , then the point P(x_1,y_1) lies on the line. (a) 6(x+y)-25=0 (b) 2x+6y+1=0 (c) 2x+3y-6=0 (d) 6(x+y)+25=0

If the points (2,\ 1) and (1,\ -2) are equidistant from the point (x ,\ y) , show that x+3y=0 .

If P(x , y) is any point on the line joining the point A(a ,0)a n dB(0, b), then show that x/a+y/b=1.

Consider the plane (x,y,z)= (0,1,1) + lamda(1,-1,1)+mu(2,-1,0) The distance of this plane from the origin is

Consider the points P(p,0,0),Q(0,q,0) and R(0,0,r) where pqr!=0 then the equation of the plane PQR is (A) px+qy+r=1 (B) x/p+y/q+z/r=1 (C) x+y+z+1/p+1/q+1/r=0 (D) none of these

If (x,y) be any point on the line segment joinijng the points (a,0)and (0,b) then prove that x/b+y/b=1.