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Question
Position vector of 4 points are given as −−→OA=2^i+3^j−^k, −−→OB=^i−2^j+3^k, −−→OC=3^i+4^j−2^k and −−→OD=^i−6^j+6^k
and O be the origin. Then,
Position vector of 4 points are given as −−→OA=2^i+3^j−^k, −−→OB=^i−2^j+3^k, −−→OC=3^i+4^j−2^k and −−→OD=^i−6^j+6^k
and O be the origin. Then,
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Solution
The correct option is B all the 4 points are coplaner
Given −−→OA=2^i+3^j−^k
−−→OB=^i−2^j+3^k
−−→OC=3^i+4^j−2^k
and −−→OD=^i−6^j+6^k
−−→AB=−^i−5^j+4^k−−→AC=^i+^j−^k−−→AD=−^i−9^j+7^k
Now
[−−→AB −−→AC −−→AD]=∣∣
∣∣−1−5411−1−1−97∣∣
∣∣=2+30−32=0
So all the 4 points are coplaner
Given −−→OA=2^i+3^j−^k
−−→OB=^i−2^j+3^k
−−→OC=3^i+4^j−2^k
and −−→OD=^i−6^j+6^k
−−→AB=−^i−5^j+4^k−−→AC=^i+^j−^k−−→AD=−^i−9^j+7^k
Now
[−−→AB −−→AC −−→AD]=∣∣ ∣∣−1−5411−1−1−97∣∣ ∣∣=2+30−32=0
So all the 4 points are coplaner
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