Geometry
Dot Product of Vectors
Find the shortest distance between the point \(P=(1,-2,3)\) and the line \[2(x-3)=y-1=z+1.\]
Find the shortest distance between the point \(P=(0,3,4)\) and the line \[x=0,\ \frac{y}{2}=-z+3.\]
Find the shortest distance between the origin and the line \[x-1=\frac{y+1}{-4}=\frac{z-7}{3}.\]
What is the shortest distance between the line \(x-2=y-1=z+1\) and the sphere \(x^2+y^2+z^2=4?\)
Find the shortest distance between the origin and the line \[\frac{x+1}{2}=-y+2=-z+2.\]