Consider the points A,B,C,D with position vectors 7^i−4^j+7^k, ^i−6^j+10^k, −^i−3^j+4^k, 5^i−^j+^k respectively. Then ABCD is a
A
Square
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B
Rhombus
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C
Parallelogram but not a rhombus
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D
Rectangle
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Solution
The correct option is A Rhombus −−→AB=−6^i−2^j+3^k −−→BC=−2^i+3^j−6^k −−→CD=6^i+2^j−3^k −−→DA=2^i−3^j+6^k −−→AB=λ−−→CD−−→BC=λ−−→DA⎛⎜⎝−−→AB∥−−→CD−−→BC∥−−→DA⎞⎟⎠ ∣∣∣−−→AB∣∣∣=∣∣∣−−→CD∣∣∣=∣∣∣−−→BC∣∣∣=∣∣∣−−→DA∣∣∣ −−→AB.−−→BC≠0 So ABCD is a Rhombus