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The points A(5, -1, 1), B(7, -4, 7),C(1 ...

The points `A(5, -1, 1), B(7, -4, 7),C(1 , -6, 10) andD (-1,-3,4)` are the vertices of a

A

trapezium

B

rectangle

C

rhombus

D

square

Text Solution

Verified by Experts

The correct Answer is:
C
If can easily be seen that `AB=BC=CD=DA=7`.
So, ABCD is a rhombus. Also, `vec(AB).vec(BC)!=0`. So AB is not perpendicular to BC. Therefore ABCD is not a square
But `vec(AC).vec(BD)=0`. Hence ABCD is a rhombus.
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OBJECTIVE RD SHARMA-THREE DIMENSIONAL COORDINATE SYSTEM -Section I - Solved Mcqs
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