 Hi and welcome to the session. Let us discuss the following question, question says, find magnitude of A vector cross B vector if A vector is equal to i minus 7j plus 7k and B vector is equal to minus 3i minus 2j plus 2k. First of all, let us understand that if vector c is equal to c1i plus c2j plus c3k and d vector is equal to d1i plus d2j plus d3k then cross product of vector c and vector d is equal to determinant of vector i, vector j, vector k, c1, c2, c3, d1, d2, d3. This is the key idea to solve the given question. Let us now start with the solution. Now we are given A vector is equal to i vector minus 7j plus 7k and B vector is equal to 3i minus 2j plus 2k. Now cross product of A vector and B vector is equal to determinant of vector i, vector j, vector k, 1 minus 7, 7, 3 minus 2, 2. Now expanding this determinant with respect to R1 we get vector i multiplied by minus 14 minus minus 14 minus vector j multiplied by 2 minus 21 plus vector k multiplied by minus 2 minus minus 21. Now this is further equal to vector i multiplied by 0 minus vector j multiplied by minus 19 plus vector k multiplied by 19. So we get vector A cross vector B is equal to 19j plus 19k. Now we will find out magnitude of A vector cross B vector it is equal to square root of 19 square plus 19 square. Now simplifying further we get square root of 361 plus 361 we know square of 19 is equal to 361. Now this is further equal to 19 multiplied by square root of 2. So we get magnitude of A vector cross B vector is equal to 19 multiplied by root 2. This is our required answer. This completes the session. Hope you understood the solution. Take care and keep smiling.