Consider the following statements in respect of a vector d = ( a b ) c : I. d is coplanar with a and b . II. d is perpendicular to c . Which of the statements given above is/are correct?

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 m