NDA Mathematics Question (2025) — Solution

Step-by-step solution

Given d = ( a b ) c Using the vector triple product expansion: d = ( a c ) b - ( b c ) a This shows that d is expressed as a linear combination of a and b . Thus, d lies in the plane containing a and b , making it coplanar with a and b . Statement I is correct. By the definition of the cross product, the vector resulting from the cross product of two vectors is perpendicular to both of them. Since d is the cross product of ( a b ) and c , it must be perpendicular to both ( a b ) and c . Therefore, d c = 0, which means d is perpendicular to c . Statement II is correct. Both statements I and II are correct. Answer: Both I and II