Questions in 3-d

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A plane meets the co-ordinate axes in $A,B,C$ and $(\alpha ,\beta ,\gamma )$ is the centered of the triangle $ABC$ . Then the equation of the plane is
If the planes $3x-2y+2z+17=0$ and $4x+3y-kz=25$ are mutually perpendicular , then $k=$
If O is the origin and A is the point (a, b, c) then the equation of the plane through A and at right angles to OA is
If from a point $P(a,b,c)$ perpendiculars $PA$ and $PB$ are drawn to yz and zx planes, then the equation of the plane $OAB$ is
The graph of the equation ${{y}^{2}}+{{z}^{2}}=0$ in three dimensional space is
A variable plane is at a constant distance p from the origin and meets the axes in A, B and C. The locus of the centroid of the tetrahedron $OABC$ is
The plane $ax+by+cz=1$ meets the co-ordinate axes in A, B and C. The centroid of the triangle is
The equation of a plane which cuts equal intercetps of unit length on the axes, is
The equation of the plane through (2, 3, 4) and parallel to the plane $x+2y+4z=5$ is
The plane $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=3$ meets the co-ordinate axes in $A,B,C$ . The centroid of the triangle ABC is

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