If a plane meets the coordinate axes at A,B,C such that the centroid of the triangle ABC is the point `(u,v,w),` find the eqution 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.

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 line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is

The vertices of Delta ABC lie on a rectangular hyperbola such that the orthocenter of the triangle is (3, 2) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. The two perpendicular tangents of the hyperbola intersect at the point (1, 1). The equation of the pair of asymptotes is

The vertices of Delta ABC lie on a rectangular hyperbola such that the orthocenter of the triangle is (3, 2) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. The two perpendicular tangents of the hyperbola intersect at the point (1, 1). The equation of the rectangular hyperbola is

A variable plane l x+m y+n z=p(w h e r el ,m ,n are direction cosines of normal ) intersects the coordinate axes at points A ,Ba n dC , respectively. Show that the foot of the normal on the plane from the origin is the orthocenter of triangle A B C and hence find the coordinate of the circumcentre of triangle A B Cdot

Find the coordinates of centroid of the triangle with vertices: (6, 2), (0, 0) and (4, -7)

A(x_1, y_1), B(x_2,y_2), C(x_3,y_3) are three vertices of a triangle ABC. lx+my+n=0 is an equation of the line L. If the centroid of the triangle ABC is at the origin and algebraic sum of the lengths of the perpendicular from O the vertices of triangle ABC on the line L is equal to, then sum of the squares of reciprocals of the intercepts made by L on the coordinate axes is equal to

A variable plane passes through a fixed point (alpha,beta,gamma) and meets the axes at A ,B ,a n dCdot show that the locus of the point of intersection of the planes through A ,Ba n dC parallel to the coordinate planes is alphax^(-1)+betay^(-1)+gammaz^(-1)=1.