Example - distance between two points

Example — Vector and distance between two points

Let $A(0;3;4)$ and $B(-1;-1;-1)$. The vector going from $A$ to $B$ is $\vec{AB} = B-A = (-1;-4;-5).$ Its length — that is, the distance between the two points — is $|\vec{AB}| = \sqrt{(-1)^2+(-4)^2+(-5)^2} = \sqrt{1+16+25} = \sqrt{42}\approx 6{,}48.$

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Topics: Analytic geometry in space
Concepts: Distance between points · Cartesian plane · Vector
Skills: Analytic geometry · Using formulae