NDA Mathematics Question (2026) — Solution

Step-by-step solution

Given a b = c and b c = a . From the properties of the cross product, c is perpendicular to both a and b . Similarly, a is perpendicular to both b and c . This implies that a , b , and c are mutually orthogonal. Thus, Statement I is correct. Since the vectors are mutually orthogonal, the angle between any two of them is 90^ . Taking the magnitude of the first equation: | a b | = | c | | a || b | = | c | Taking the magnitude of the second equation: | b c | = | a | | b || c | = | a | Substituting | c | from the first equation into the second: | b |(| a || b |) = | a | | a || b |^2 = | a | For non-zero vectors, we get | b |^2 = 1 | b | = 1. This gives | a | = | c |. However, | a | and | c | can be any positive real number and are not necessarily equal to 1. Thus, Statement II is incorrect.