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# Dot Product of Vectors

The dot product (also known as the scalar product) is an operation on vectors that can tell you the angle between the vectors.

# Dot Product - Distance between Point and a Line

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 $\frac{x+1}{2}=-y+2=-z+2.$

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