Questions in 3-d

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The points $A(-1,3,0)$ , $B\,(2,\,2,\,1)$ and $C\,(1,\,1,\,3)$ determine a plane. The distance from the plane to the point $D(5,\,7,8)$ is
In a three dimensional xyz space the equation ${{x}^{2}}-5x+6=0$ represents
The equations $|x|=p,|y|=p,|z|=p$ in xyz space represent
In the space the equation $by+cz+d=0$ represents a plane perpendicular to the plane
The equation of the plane through the point (1, 2, 3 ) and parallel to the plane $x+2y+5z=0$ is
The equation of the plane passing through the intersection of the planes $x+2y+3z+4=0$ and $4x+3y+2z+1=0$ and the origin is
The equation of the plane passing through (2, 3, 4) and parallel to the plane $5x-6y+7z=3$
The distance of the plane $6x-3y+2z-14=0$ from the origin is
The value of $aa'+\,bb'+\,cc'$ being negative the origin will lie in the acute angle between the planes $an+by+cz+d=0$ and $a'x+b'y+c'z+d'=0$ , if
The equation of the plane passing through (1, 1, 1) and (1, –1, –1) and perpendicular to $2x-y+z+5=0$ is

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