A) A rectangle
B) A square
C) A parallelogram
D) None of these
Correct Answer: D
Solution :
Let \[A(5,\,-4,\,2)\],\[B(4,\,-3,\,1),\]\[C(7,\,-6,\,4)\] and \[D(8,\,-7,\,5)\]. Then \[AB=\sqrt{1+1+1}=\sqrt{3}\], \[BC=\sqrt{9+9+9}=3\sqrt{3}\], \[CD=\sqrt{1+1+1}=\sqrt{3}\] \[AD=\sqrt{9+9+9}=3\sqrt{3}\]. But \[\overrightarrow{AB}\,.\,\overrightarrow{BC}\ne 0\] Let the angle between AB and BC be \[\theta \], then \[\cos \theta =-1\Rightarrow \theta =\pi \]. Hence option is correct.You need to login to perform this action.
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