For all real x, the vectors Cx i -6 j -3 k and x i +2 j -2Cx k make an obtuse angle with each other then the value of C can be in

MHT CET 2024 Mathematics question

For all real x, the vectors and make an obtuse angle with each other then the value of C can be in

(A)(0,1)
(B)
(C)Correct
(D)

Answer: (C)

Solution

The angle is obtuse when the dot product is negative: (Cx)(x)+(-6)(2)+(-3)(-2Cx)=Cx^2+6Cx-12<0 for all real . A quadratic is negative for every when and the discriminant is negative: (for the expression is as

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Question ID VK-092853