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## 3D Coordinate Geometry

Append a z-axis to the 2-dimensional plane and conquer the realm of 3-dimensional space.

# Distance

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

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

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

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

What is the square of the distance between the two lines \begin{align} l&:~x-9=y-8=z-4,\\ m&:~x-10=y-10=z-7? \end{align}

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