Passage: Let a b = c and b c = a . Question: Consider the following statements : I. a , b , c are orthogonal in pairs. II. a , b , c are unit vectors. Which of the statements given above is/are correct ?

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