 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that, find the area of the parallelogram having dinos vector a is equal to 2i cap plus j cap minus 3k cap and vector b is equal to i cap minus 2j cap plus k cap. We know that area of the parallelogram whose dinos are given is equal to 1 by 2 into area of the parallelogram whose adjacent sides are the dinos of the given parallelogram and area of the parallelogram whose adjacent sides are given by vector a and vector b is equal to modulus of vector a cross vector b. With this idea let us proceed with the solution. Here in this question vector a is given as 2i cap plus j cap minus 3k cap and vector b is given as i cap minus 2j cap plus j cap and we need to find the area of the parallelogram having dinos that is vector a and vector b are given and from the key idea we know that area of the parallelogram whose dinos are given is equal to 1 by 2 into area of the parallelogram whose adjacent sides are the dinos of the given parallelogram and area of the parallelogram whose adjacent sides are vector a and vector b is given by modulus of vector a cross vector b. So now we shall find out the area of the parallelogram taking vector a and vector b as the adjacent sides. So vector a cross vector b is equal to the determinant containing elements i cap j cap k cap 2 1 minus 3 1 minus 2 1. On solving this we get i cap into 1 into 1 that is 1 minus of minus 2 into minus 3 that is 6 minus of j cap into 2 into 1 that is 2 minus of 1 into minus 3 that is minus 3 plus j cap into 2 into minus 2 that is minus 4 minus of 1 into 1 that is 1 which is equal to i cap into 1 minus 6 that is minus 5 minus of j cap into 2 minus of minus 3 that is 2 plus 3 which is equal to 5 plus k cap into minus 4 minus 1 that is minus 5. Therefore vector a cross vector b is equal to minus 5 into i cap minus 5 into j cap minus 5 into k cap and the value of modulus of vector a cross vector b is given by square root of minus 5 d whole square plus of minus 5 d whole square which is equal to square root of minus 5 d whole square that is 25 plus minus 5 d whole square that is 25 plus minus 5 d whole square that is 25 which is equal to Therefore, modulus of vector A cross vector B is equal to square root of 75 which is equal to 5 into square root of 3. Therefore, the area of the parallelogram whose adjacent sites are given by vector A and vector B is equal to 5 into square root of 3 square units hence the area of the given parallelogram 1 by 2 into area of the parallelogram whose adjacent sites are the diagonals of the given parallelogram that is equal to 1 by 2 into 5 into square root of 3 square units which is equal to 5 into square root of 3 by 2 square units therefore the required area of the given parallelogram is 5 into square root of 3 by 2 square units which is the required answer. This completes our session. Hope you enjoyed this session.