 Hello and welcome to the session. In this session we are going to discuss the following question which says that if vector a is equal to i cap minus j cap plus 3 k cap, vector b is equal to 5 i cap plus 3 j cap plus 2 k cap, vector c is equal to 2 i cap plus 2 j cap minus k cap, simply 5 scalar triple product of vectors a minus b b minus c c minus a. Let's start the solution. Vector a is given by i cap minus j cap plus 3 k cap, vector b is given by 5 i cap plus 3 j cap plus 2 k cap, vector c is given by 2 i cap plus 2 j cap minus k cap. Next we shall find vector a minus vector b which is given by i cap minus j cap plus 3 k cap minus of 5 i cap plus 3 j cap plus 2 k cap which is equal to i cap minus 5 i cap that is minus 4 i cap minus j cap minus 3 j cap that is minus 4 j cap plus 3 cap minus 2 k cap that is plus k cap. So vector a minus vector b is equal to minus 4 i cap minus 4 j cap plus k cap. Now we shall find vector b minus vector c which is equal to 5 i cap plus 3 j cap plus 2 k cap minus of 2 i cap plus 2 j cap minus k cap which is equal to 5 i cap minus 2 i cap that is 3 i cap plus 3 j cap minus 2 j cap that is plus j cap plus 2 k cap minus of minus k cap that is plus 3 k cap. So vector b minus vector c is equal to 3 i cap plus j cap plus 3 k cap and vector c minus vector a is given by 2 i cap plus 2 j cap minus k cap minus of i cap minus j cap plus 3 k cap which is equal to 2 i cap minus i cap that is i cap plus 2 j cap minus of minus j cap that is plus 3 j cap minus k cap minus of 3 k cap that is minus 4 k cap. So vector c minus vector a is given by i cap plus 3 j cap minus 4 k cap. Now we have vector a minus vector b is equal to minus 4 i cap minus 4 j cap plus k cap. Vector b minus vector c is equal to 3 i cap plus j cap plus 3 k cap and vector c minus vector a is equal to i cap plus 3 j cap minus 4 k cap. Now scalar triple product of vectors a minus b, b minus c, c minus a is given by the determinant of vector a minus b, b minus c and c minus a which is equal to minus 4 into 1 into minus 4 that is minus 4 minus of 3 into 3 that is minus 4 into 3 into minus 4 that is minus 12 minus of 1 into 3 that is 3 plus 1 into 3 into 3 that is 9 minus of 1 into 1 that is 1 which is equal to minus 4 into minus 13 plus 4 into minus 15 plus 1 into 8 which is equal to 52 minus 60 plus 8 which is equal to 60 minus 60 that is 0. Therefore, the scalar triple product of vectors a minus b, b minus c, c minus a is equal to 0 which is the required answer. This completes our session. Hope you enjoyed this session.