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

Step-by-step solution

To ensure the angle between vectors p =my i -6 j +3 k and q =y i +2 j +2my k is obtuse , the dot product must satisfy p q my^2 + 6my - 12 For this quadratic inequality to hold for all real y , the coefficient of y^2 must be negative and the discriminant must be negative. m Factoring gives 12m(3m + 4) Combining both conditions yields the range -4/3 The correct option is D.