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Question

Consider points A,B,C,D with position vectors 7^i4^j+7^k, ^i6^j+10^k, ^i3^j+4^k and 5^i^j+5^k respectively. Then ABCD is a

A
Rhombus
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B
Rectangle
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C
Parallelogram but not a rhombus
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D
None of these
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Solution

The correct option is C None of these
We have
A=(7,4,7) B=(1,6,10)
C=(1,3,4) D=(5,1,5)

Lets find
AB=(6,2,3) |AB|=7
BC=(2,3,6) |BC|=7
CD=(6,2,1) |CD|=41
DA=(2,3,2) |DA|=17
Its None of these

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