1.

If the vectors `veca = ( c log_(2) x ) hatk ` make an obtuse angle for any ` x ne ( 0 , oo) ` then c belongs toA. ` ( - oo, 0)`B. ` ( - oo , -4//3)`C. ` ( -4//3,0)`D. ` (-4//3, oo)`

Answer» Correct Answer - C
For the vectors ` veca and vecb` to be inclined at an obtuse angle we must have
` veca. Vecb lt o) " for all " x ne ( 0, oo)`
` Rightarrow 2(log_(2) x) ^(2) - 12 + 6 c ( log_(2) x ) lt 0 " for all " x ne ( 0, oo)`
` Rightarrow 2y^(2) + 6 cy -12 lt 0 " for all " y ne R, " where " y = log_(2) x `
` Rightarrow c lt 0 and 36 c^(2) + 48 c lt 0`
` Rightarrow c lt 0 and c ( 3c + 4) lt 0`
` c lt 0 and - 4/3 lt c lt 0`
` Rightarrow c in ( -4//3 , 0)`


Discussion

No Comment Found

Related InterviewSolutions