Question

For two n-dimensional real vectors P and Q
$thenoperations(P,Q)isdefinedasfollows:$
$s(P,Q)=\sum _{i-1}^n\left(P\right[i].Q[i\left]\right)$
Let L be a set of 10 dimensional non-zero real vectors such that for every pair of distinct vector
$P,QϵL,s(P,Q)=0$.
What is the maximum cardinality possible for the set L?

• A. 10
• B. 11
• C. 100
• D. 9

Answer 1

The correct option is A 10

L is the set of 10-dimensional orthogonal vectors.
So cardinality of $L\le 10$
i.e., Maximum cardinality of $L=10$
So, option (a) is correct.