A plane passing through `(1,1,1)` cuts positive direction of coordinates axes at `A ,Ba n dC ,` then the volume of tetrahedron `O A B C` satisfies a. `Vlt=9/2` b. `Vgeq9/2` c. `V=9/2` d. none of these

A variable plane passes through a fixed point (a ,b ,c) and cuts the coordinate axes at points A ,B ,a n dCdot Show that locus of the centre of the sphere O A B Ci s a/x+b/y+c/z=2.

Find the equation of a plane passing through (1, 1, 1) and parallel to the lines L_1 and L_2 direction ratios (1, 0,-1) and (1,-1, 0) respectively. Find the volume of the tetrahedron formed by origin and the points where this plane intersects the coordinate axes.

The number of real solutions of the equation (9//10)^x=-3+x-x^2 is a. 2 b. 0 c. 1 d. none of these

Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

If a plane cuts off intercepts OA = a, OB = b, OC = c from the coordinate axes 9where 'O' is the origin). then the area of the triangle ABC is equal to

If a ,b , a n dc are in G.P. and x ,y , respectively, are the arithmetic means between a ,b ,a n db ,c , then the value of a/x+c/y is 1 b. 2 c. 1//2 d. none of these

If a plane meets the equations axes at A ,Ba n dC such that the centroid of the triangle is (1,2,4), then find the equation of the plane.

If a plane meets the equations axes at A ,Ba n dC such that the centroid of the triangle is (1,2,4), then find the equation of the plane.

A variable plane passes through a fixed point (a,b,c) and meets the axes at A ,B ,a n dCdot The locus of the point commom to the planes through A ,Ba n dC parallel to the coordinate planes is