Geometry

Dot Product of Vectors

Dot Product - Distance between Point and a Line

         

Find the shortest distance between the point P=(1,2,3)P=(1,-2,3) and the line 2(x3)=y1=z+1.2(x-3)=y-1=z+1.

Find the shortest distance between the point P=(0,3,4)P=(0,3,4) and the line x=0, y2=z+3.x=0,\ \frac{y}{2}=-z+3.

Find the shortest distance between the origin and the line x1=y+14=z73.x-1=\frac{y+1}{-4}=\frac{z-7}{3}.

What is the shortest distance between the line x2=y1=z+1x-2=y-1=z+1 and the sphere x2+y2+z2=4?x^2+y^2+z^2=4?

Find the shortest distance between the origin and the line x+12=y+2=z+2.\frac{x+1}{2}=-y+2=-z+2.

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