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Question: The points \(A ( 5 , - 1,1 )\) ; \(B ( 7 , - 4,7 )\) \(C ( 1 , - 6,10 )\) and \(D ( - 1 , - 3...

The points A(5,−1,1)A ( 5 , - 1,1 ) ; B(7,−4,7)B ( 7 , - 4,7 ) C(1,−6,10)C ( 1 , - 6,10 ) and

D(−1,−3,4)D ( - 1 , - 3,4 ) are vertices of a

A

Square

B

Rhombus

C

Rectangle

D

None of these

Answer

Rhombus

Explanation

Solution

∙∙\bullet \bullet AB=BC=CD=DA=7A B = B C = C D = D A = 7 . Also AB→⋅BC→≠0\overrightarrow { A B } \cdot \overrightarrow { B C } \neq 0

∴ ABCD is not square. It is rhombus.