 Hi and welcome to the session. Let us discuss the following question. Question says, find the area of the parallelogram whose adjacent sides are determined by the vectors vector a is equal to i minus j plus 3k and vector b is equal to 2i minus 7j plus k. Let us now start with the solution. Now we know we have to find the area of a parallelogram and adjacent sides of parallelogram are determined by vector a and vector b and vector b is equal to 2i minus 7j plus k and vector a is equal to 2i minus j plus 3k. Now we know the area of a parallelogram with adjacent sides vector a and vector b is equal to magnitude of vector a cross vector b. Now to find the area of a parallelogram first of all we will find cross product of vector a and vector b. It is equal to determinant of unit vector i, unit vector j, unit vector k, 1 minus 1, 3, 2 minus 7, 1. Now expanding this determinant with respect to this row we get vector i multiplied by minus 1 minus minus 21 minus unit vector j multiplied by 1 minus 6 plus unit vector k multiplied by minus 7 minus minus 2. Now simplifying further we get 20i plus 5j minus 5k is equal to a vector cross b vector. Now magnitude of a vector cross b vector is equal to square root of 20 square plus 5 square plus minus 5 square. Now this is further equal to square root of 400 plus 25 plus 25. Now adding these three terms we get square root of 450. Now this is further equal to 15 root 2. So we get magnitude of a vector cross b vector is equal to 15 root 2. Now we know magnitude of a vector cross b vector is equal to area of a parallelogram. So area of a given parallelogram is equal to 15 root 2. So this is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.