 Hi, and welcome to the session. Let's work out the following question. The question says, given that vector a is equal to i cap plus j cap, vector b is equal to j cap minus 3k cap, and vector c is equal to i cap plus 4k cap, verify that vector a cross vector b cross vector c is equal to vector a dot vector c into vector b minus vector a dot vector b into vector c. So, let us see the solution to this question. Here vector a is equal to i cap plus j cap, vector b is equal to j cap minus 3k cap, and vector c is equal to i cap plus 4k cap. Therefore, vector b cross vector c is equal to the determinant i cap j cap k cap, 0, 1, minus 3, 1, 0, 4. That is equal to i cap into 4, minus j cap into 4, 0's are 0, minus minus 3, plus k cap into minus 1. So, this is equal to 4 i cap minus 3j cap minus k cap. Now, l h is that is left hand side will be equal to vector a cross vector b cross vector c. That is i cap plus j cap cross 4i cap minus 3j cap minus k cap. That is equal to the determinant i cap j cap k cap 1, 1, 0, 4, minus 3, minus 1. That is equal to i cap into minus 1, minus j cap into 1 into minus 1 is minus 1, plus k cap into minus 3, minus 4. So, this is equal to minus i cap plus j cap minus 7 k cap. We call this 1. Now, we consider vector a dot vector c that will be equal to i cap plus j cap into or dot vector. This is i cap plus 4 k cap. This is equal to i cap dot i cap plus 4 i cap dot k cap plus j cap dot i cap plus 4 j cap dot k cap. That is equal to 1 plus 0 plus 0 plus 0. That is equal to 1. And vector a dot vector b is equal to i cap plus j cap dot j cap minus 3 k cap. That is equal to vector i dot vector j. That is 0. minus 3 j cap dot k cap. Sorry, this is i cap into j cap is 0 plus j cap dot j cap is 1 plus i cap dot j cap is 0 and this will also be 0. So again we have 1. Now right-hand side is vector a dot vector c into vector b minus vector a dot vector b into vector c. This is equal to 1 into j cap minus 3 k cap minus 1 into i cap plus 4 k cap. That is equal to j cap minus 3 k cap minus i cap minus 4 k cap which is equal to minus i cap plus j cap minus 7 k cap. We call this 2. So from equation 1 and equation 2, we get LHS is equal to RHS or we can say that vector a cross vector v cross vector c is equal to vector a dot vector c into vector b minus vector a dot vector b into vector c. So this is what we were supposed to prove in this question. I hope that you understood the solution and enjoyed the session. Have a good day.