Vector, magnitude and midpoint

Statement

Given $A(1;2;3)$ and $B(-1;0;5)$, calculate $\vec{AB}$, $|\vec{AB}|$ and the midpoint of the segment $AB$.

Solution

$\vec{AB} = B-A = (-2;-2;2).$ $|\vec{AB}| = \sqrt{(-2)^2+(-2)^2+2^2} = \sqrt{12} = \boxed{2\sqrt3}.$ $M = \left(\frac{1-1}{2};\;\frac{2+0}{2};\;\frac{3+5}{2}\right) = \boxed{(0;\,1;\,4)}.$

Links

Topics: Analytic geometry in space
Concepts: Distance between points · Cartesian plane · Midpoint · Vector
Skills: Calculating · Analytic geometry · Using formulae
Exercise types: Geometric problem