If the vectors →a=(clog2x)^i−6^j+2^k and →b=(log2x)^i+2^j+3(clog2x)^k make an obtuse angle for any x∈(0,∞) then c belongs to
Options:
A .  
(−∞,0)
B .  
(−∞,−43)
C .  
(−43,0)
D .  
(−43,∞)
Answer: Option C : C For the vectors →a and →b to be inclined at an obtuse angle, we must have →a.→b<0 for all x∈(0,∞) ⇒c(log2x)2−12+6c(log2x)<0 for all x∈(0,∞) ⇒cy2+6cy−12<0 for all y∈R, where y=log2x ⇒c<0 and ⇒36c2+48c<0⇒c<0and c(3c+4)<0 ⇒c<0 and −43<c<0 ⇒c∈(−43,0)
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