 Hi and welcome to the session. Let us discuss the following question. Question says, area of a rectangle having vertices a, b, c and d with position vectors minus i plus 1 upon 2j plus 4k, i plus 1 upon 2j plus 4k, i minus 1 upon 2j plus 4k and minus i minus 1 upon 2j plus 4k respectively is a, 1 upon 2, b, 1, c, 2, d, 4. We have to choose the correct answer from a, b, c and d. Let us now start with the solution. Now we are given position vectors of a, b, c and d. We know position vector of vertex a is equal to minus i plus 1 upon 2j plus 4k position vector of vertex b is equal to i plus 1 upon 2j plus 4k. Similarly, position vector of vertex c is i minus 1 upon 2j plus 4k. Now position vector of vertex d is equal to minus i minus 1 upon 2j plus 4k. First of all, we will find out vector a, b. We know vector a, b is equal to position vector of b minus position vector of a. Now position vector of b is equal to i vector plus 1 upon 2j plus 4k. Now we will write this minus sign as it is and here we will write position vector of a. It is minus i plus 1 upon 2j plus 4k. Now subtracting the two vectors, we get 2i plus 0j plus 0k or we can simply write vector a, b is equal to 2i. Now in rectangle a, b adjacent side of vector a, b is vector b, c. Now we will find out vector b, c. We know vector b, c is equal to position vector of c minus position vector of b. Now position vector of c is i minus 1 upon 2j plus 4k. Now we will write this minus sign as it is and here we will write position vector of b. Now position vector of b is i plus 1 upon 2j plus 4k. Now subtracting corresponding components of these two vectors, we get minus j. So bc vector is equal to minus j. Now area of a rectangle with adjacent sides a, b vector and bc vector is equal to magnitude of a, b vector cross bc vector. Now we know vector a, b is equal to 2i and vector bc is equal to minus j. Now magnitude of 2i cross minus j is equal to magnitude of minus 2 multiplied by unit vector i cross unit vector j. Here we have used this property of vector product. Now applying this property of vector product here we get this expression is equal to magnitude of minus 2k. Now magnitude of k is equal to square root of minus 2 square which is further equal to square root of 4. Now this is further equal to 2. We know we are finding out area of a rectangle and area of a rectangle cannot be negative. So we will neglect minus 2 and we get 2 here. So we get area of rectangle a, b, c, d is equal to 2. So the correct answer is c. This is our required answer. This completes the session. Hope you understood the solution. Take care and keep smiling.