Question
The three points whose position vectors are ^i+2^j+3^k,3^i+4^j+7^k and−3^i−2^j−5^k
Answer: Option C
:
C
If A, B, C are the given points respectively, then
−−→OA=^i+2^j+3^k,−−→OB=3^i+4^j+7^k,−−→OC=−3^i−2^j−5^k,−−→AB=−−→OB−−−→OA=2^i+2^j+4^k,−−→AC=−−→OC−−−→OA=−4^i−4^j−8^k=−2−−→AB
∴−−→AB,−−→AC are collinear ⇒A,B,C are collinear.
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:
C
If A, B, C are the given points respectively, then
−−→OA=^i+2^j+3^k,−−→OB=3^i+4^j+7^k,−−→OC=−3^i−2^j−5^k,−−→AB=−−→OB−−−→OA=2^i+2^j+4^k,−−→AC=−−→OC−−−→OA=−4^i−4^j−8^k=−2−−→AB
∴−−→AB,−−→AC are collinear ⇒A,B,C are collinear.
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