Geometry

3D Coordinate Geometry

3D Coordinate Geometry - Distance

         

What is the distance between the point P=(1,2,3)P=(1,-2,3) and the plane x2y+3z28=0?x-2y+3z-28=0?

What is the shortest distance between the point P=(3,3,2)P=(-3,3,2) and the sphere x2+(y6)2+(z+1)2=1?x^2+(y-6)^2+(z+1)^2=1?

Find the square of distance between the point M0(0,1,3) M_{0}(0, 1, 3) and the line x42=y7=z+12.\frac{ x-4 }{2} = y-7 = \frac{ z+1}{2}.

If the distance of a point PP other than the origin from the plane x+y+z=3x+y+z=3 is equal to the distance of the plane from the origin, which of the following can be the point P?P ?

What is the square of the distance between the two lines l: x9=y8=z4,m: x10=y10=z7?\begin{aligned} l&:~x-9=y-8=z-4,\\ m&:~x-10=y-10=z-7? \end{aligned}

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