Consider the set of eight vectors V = a i + b j + c k : a, b, c -1, 1 . Three non-coplanar vectors can be chosen from V in 2^p ways. Then p is

JEE Advanced 2013 Mathematics question

Consider the set of eight vectors . Three non-coplanar vectors can be chosen from V in ways. Then p is

Answer: 5

Solution

The eight vectors are the four body diagonals of a cube, each in two opposite directions (pairs ). Three vectors are coplanar if two of them lie along the same diagonal (a vector and its negative). Any three vectors along three different diagonals are

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Question ID VK-026183