The three points whose position vectors are ^i+2^j+3^k,3^i+4^j+7^kand−3^i−2^j−5^k
Options:
A .  
form the vertices of an equilateral triangle
B .  
form the vertices of a right angled triangle
C .  
are collinear
D .  
form the vertices of an isosceles triangle.
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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