Let p = 2 i + j + 3 k and q = i - j + k . If for some real numbers , , and , we have 15 i + 10 j + 6 k = (2 p + q ) + ( p - 2 q ) + ( p q ), then the value of is _____.

JEE Advanced 2024 Mathematics question

Let and . If for some real numbers , and , we have

15 + 10 + 6 = α(2 + ) + β( - 2) + γ( × ),

then the value of is .

Answer: 2

. This vector is perpendicular to both and , so taking the dot product of the given

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Question ID VK-034225