(Exact and approximate length between fractional coordinates)

MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Three-Dimensional Geometry · Introduction to Three-Dimensional Geometry

Problem

(Exact and approximate length between fractional coordinates) (i) For the points

A\left(-2,\dfrac{5}{2},3\right)

and

B\left(4,-\dfrac{1}{2},-2\right)

, calculate

AB^{2}

leaving your answer as a single rational number. (ii) Hence determine the exact value of

AB

and also give a decimal approximation correct to two places of decimals.