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Verify the following: (5,-1,1),(7,-4,7),...

Verify the following: (5,-1,1),(7,-4,7), (1,-6,10) and (-1,-3,4) are the vertices of a rhombus.

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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