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Dot Product of Vectors

Dot Product - Distance between Point and a Line

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

5

\sqrt{29}

\sqrt{35}

6

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by Brilliant Staff

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

\sqrt{3}

2

\sqrt{5}

\sqrt{6}

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

2\sqrt{3}

4

2\sqrt{5}

5

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by Brilliant Staff

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

\frac{2\sqrt{10}}{3}-2

\frac{\sqrt{42}}{3}-2

\sqrt{5}-2

\frac{4\sqrt{3}}{3}-2

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

\frac{\sqrt{5}}{5}

\sqrt{2}

\sqrt{3}

\sqrt{6}

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