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GATE | GATE CS 2021 | Set 2 | Question 47

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  • Last Updated : 23 May, 2021

For two n-dimensional real vectors P and Q, the operation s(P,Q) is defined as follows:

Let L be a set of 10-dimensional non-zero real vectors such that for every pair of distinct vectors P,Q∈L, s(P,Q)=0. What is the maximum cardinality possible for the set L?
(A) 9
(B) 10
(C) 11
(D) 100

Answer: (B)

Explanation: s(P,Q) is the sum of dot products of vectors P and Q in each dimension.
The 0 dot product indicates that the vectors must be orthogonal to each other.

In a n-dimensional space, we have n axes orthogonal to each other.
It is given that for every pair the dot product must be 0, then at most n vectors each mentioning each dimension can be considered.

Thus for 10 dimensional space’s set of vectors ℒ , 10 mutually orthogonal vectors can be present.

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