(i) Explain why, when comparing the lengths of two line segments joining pairs of…
MATHEMATICS · Subjective · CBSE · Mathematics · Introduction to Three-Dimensional Geometry · Introduction to Three-Dimensional Geometry
Problem
(i) Explain why, when comparing the lengths of two line segments joining pairs of points in three–dimensional space, it is sufficient to compare the numerical values of the squares of those lengths.
(ii) Using the reasoning stated in part (i), consider the points A(1,2,0), B(4,−2,0) and C(1,2,3). Without evaluating any square roots, decide which of the three segments AB, AC and BC is the shortest and which is the longest. Show all working.