請教一題空間向量

設 \(\vec{AB}=\left(x,y,z\right)\)

則 \(x^2+y^2=64, x^2+z^2=36\)

\(y^2=64-x^2\geq0, z^2=36-x^2\geq0\)

\(\Rightarrow0\leq x^2\leq 36\)

\(\overline{AB}^2=x^2+y^2+z^2=100-x^2\Rightarrow 8\leq\overline{AB}\leq10\)