Passage: P(-2,-3,5) , Q(4,-1,5) , R(6,-4,8) and S(2,-6,10) are four points. Question: Consider the following statements : I. PQ is parallel to RS . II. PR is perpendicular to QS . Which of the statements given above is/are correct ?

Step-by-step solution

The direction ratios of the line segment PQ are 4 - (-2), -1 - (-3), 5 - 5 , which gives 6, 2, 0 . The direction ratios of the line segment RS are 2 - 6, -6 - (-4), 10 - 8 , which gives -4, -2, 2 . Since the ratios of their corresponding direction ratios are not equal ( 6 -4 2 -2 0 2 ), PQ is not parallel to RS . Thus, Statement I is incorrect. The direction ratios of the line segment PR are 6 - (-2), -4 - (-3), 8 - 5 , which gives 8, -1, 3 . The direction ratios of the line segment QS are 2 - 4, -6 - (-1), 10 - 5