Questions in 3-d

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If a plane meets the co-ordinate axes at A,B and C such that the centroid of the triangle is (1, 2, 4) then the equation of the plane is
If for a plane, the intercepts on the coordinate axes are 8, 4, 4 then the length of the perpendicular from the origin on to the plane is
The point at which the line joining the points (2, –3, 1) and (3, –4, –5) intersects the plane $2x+y+z=7$is
The point of intersection of the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z+2}{3}$ and the plane $2x+3y+z=0$is
The line $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{0}$is parallel to
The equation of the plane passing through the origin and perpendicular to the line $x=2y=3z$is
If the equation of a line and a plane be $\frac{x+3}{2}=\frac{y-4}{3}=\frac{z+5}{2}$and$4x-2y-z=1$respectively, then
The equation of the straight line passing through (1, 2, 3) and perpendicular to the plane $x+2y-5z+9=0$ is
The equation of the plane passing through the lines $\frac{x-4}{1}=\frac{y-3}{1}=\frac{z-2}{2}$and $\frac{x-3}{1}=\frac{y-2}{-4}=\frac{z}{5}$ is
The equation of the plane passing through the points (3,2,2) and (1,0,–1) and parallel to the line $\frac{x-1}{2}=\frac{y-1}{-2}=\frac{z-2}{3}$, is

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