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 `0

If points (a,0),(0,b) and (x,y) are collinear, using the concept of slope prove that (x)/(a)+(y)/(b)=1

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

A straight line joining the points (1,1,1) and (0,0,0) intersect the plane 2x+2y+z=10 at

If each of the points (x_(1),4),(-2,y_(1)) lies on the line joining the points (2,-1) and (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

Show that the points (-3,0,1) and (1,1,1) are equidistant from the plane 3x+4y-12z+13=0 .

Let pi be the plane parallel to y-axis and containing the points (1,0,1) and (3,2,-1) .Also A=(4,0,0) and B=(6,0,-2) are two points and P=(x_(0),y_(0),z_(0)) is a variable point on the plane pi=0.

Curves y=f(x) passing through the point (0,1) and y=int_-oo^x f(t) dt passing through the point (0,1/3) are such that the tangents drawn to them at the point with equal abscissae intersect on x-axis. Answer the question:The area bounded by the curve y=f(x), y=x and ordinates x=0 and x=1 is (A) (e^2-1)/2 (B) (e^2-1)/3 (C) (e^3-1)/3 (D) none of these

If O(0, 0, 0), A(x, 1, -1), B(0, y, 2) and C(2, 3, z) are coplanar, then

Distance between the point (0,1,7) and the plane 3x + 4y + 1 = 0 is :

then image of the point (-1,3,4) in the plane x-2y=0