(Distance involving surd coordinates)

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

Problem

(Distance involving surd coordinates) (i) Compute the distance between the points

P(\sqrt{3},2,-1)

and

Q(-\sqrt{3},-4,5)

, expressing your answer in its simplest surd form. (ii) If one unit of length in the coordinate system represents

10\,\text{cm}

, express the distance obtained in part (i) in centimetres correct to one decimal place.