The value of m R, when angle between the vectors p=my i-6 j+3 k and q=y i+2 j+2my k is obtuse angle, is

MHT CET 2025 Mathematics question

The value of , when angle between the vectors and is obtuse angle, is

(A)
(B)m = 0
(C)m > 0
(D)Correct

Answer: (D)

Solution

The angle is obtuse iff (and the vectors are not antiparallel). \bar p\cdot\bar q=my^2-12+6my=my^2+6my-12. For this to be negative for every real y we need the quadratic to lie below the y-axis: leading coefficient and discriminant :

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Question ID VK-101847