question_answer

Consider points A, B, C and D with position vectors  \[7\hat{i}-4\hat{j}+7\hat{k}\], \[\hat{i}-6\hat{j}+10\hat{k}\], \[-\hat{i}-3\hat{j}+4\,\hat{k}\]and \[5\,\hat{i}-\hat{j}+5\,\hat{k}\], respectively. Then, ABCD is a     AIEEE  Solved  Paper-2003

A)                                         square                 

B)       rhombus

C) rectangle            

D) parallelogram but not a rhombus None of the given option is correct.

Correct Answer: D

Solution :

Given, ,              ,  and Now,         \[AB=\sqrt{{{(7-1)}^{2}}\,+{{(-4+6)}^{2}}+{{(7-10)}^{2}}}\]                                                                                                                                                                             and                                Thus, no option is correct.