2
Question
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
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
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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
−−→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
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