 Hi and welcome to the session. Let us discuss the following question. Question says, if either A vector is equal to 0 vector or B vector is equal to 0 vector, then A vector cross B vector is equal to 0 vector. Is the converse true? Justify your answer with an example. Let us now start with the solution. Now the given statement is, if either vector A is equal to 0 vector or vector B is equal to 0 vector, then A vector cross B vector is equal to 0 vector. First of all, let us write the converse of this statement. Converse of this statement says, if A vector cross B vector is equal to 0 vector, then either A vector or B vector is a 0 vector. Now this is the converse of the given statement. Now if A vector and B vector both are non-zero vectors and their cross product is equal to 0 vector, then both of these vectors are parallel to each other. So here we can write or else A vector is parallel to B vector. So we can say converse of this statement is not true. Clearly we can see this statement is incomplete. So we will add or else A vector is parallel to B vector here to complete this statement. So we can say converse of this statement is not true. Now let us take one example to justify this statement. Let vector A is equal to 9i plus 6j plus 27k and B vector is equal to 3i plus 2j plus 9k. Now cross product of A vector and B vector is given by determinant of unit vector i, unit vector j, unit vector k, 9, 6, 27, 3, 2, 9. Now expanding this determinant with respect to this row, we can write unit vector i multiplied by 54 minus 54 minus unit vector j multiplied by 81 minus 81 plus unit vector k multiplied by 18 minus 18. Now this is equal to 0i minus 0j plus 0k or we can simply write this vector as 0 vector. So we get A vector cross B vector is equal to 0 vector. Clearly we can see magnitude of A vector and magnitude of B vector is not equal to 0. Now we can write magnitude of vector A is not equal to 0 and magnitude of vector B is also not equal to 0 and vector A is equal to 3 multiplied by 3i plus 2j plus 3k. Here we can see all these numbers are multiples of 3. So we can take 3 common from every component of vector A. Now these are the components of vector B. So we can write A vector is equal to 3 multiplied by B vector. Now from this equation we get vector A and vector B are collinear vectors. We know if A vector is equal to lambda times B vector where lambda is some scalar quantity then A vector and B vector are collinear vectors. Now in this equation value of lambda is 3. So A vector and B vector are collinear vectors. Now we know collinear vectors are vectors which are parallel to the same line. So here we can write A vector is parallel to B vector. Now clearly we can see if we consider two non-zero collinear vectors and find out their cross product then their cross product is equal to 0 or we can say if A vector is parallel to B vector then cross product of two vectors is equal to 0 vector. So we get no converse of the given statement is not true. This is our required answer. This completes the session. Hope you understood the solution. Take care and keep smiling.