 Hi and welcome to the session. Let's work out the following question. The question says show that four points A, B, C and D whose position vectors are 6i cap minus 7j cap, 16i cap minus 19j cap minus 4k cap, 3j cap minus 6k cap and 2i cap minus 5j cap plus 10k cap respectively are coplanar. So let's start with the solution to this question. Let A, B, C and D be four points whose position vectors referred to origin O, R vector O, A is equal to 6i cap minus 7j cap, vector O, B is equal to 69 cap minus 19j cap minus 4k cap, vector O, C is equal to 3j cap minus 6k cap and vector O, D is equal to 2i cap minus 5j cap plus 10k cap. Therefore, vector A, B will be equal to vector O, B minus vector O, A that is equal to 69 cap minus 19j cap minus 4k cap minus 6i cap minus 7j cap. This is equal to, now 16i cap minus 6i cap is 10i cap minus 19j cap plus 7j cap is minus 12j cap minus 4k cap. Similarly, vector AC is equal to vector OC minus vector O, A that is equal to 3i cap minus 6j cap, sorry this is 6k cap minus vector O, A that is 6i cap minus 7j cap and this is equal to, now 3i cap minus 6j cap, sorry this is 3j cap minus 6k cap, so we get minus 6i cap plus 10j cap minus 6k cap. Similarly, we have vector AD is equal to vector OD minus vector O, A that is equal to 2i cap minus 5j cap plus 10k cap minus 6i cap minus 7j cap that is equal to minus 4i cap plus 2j cap plus 10k cap. Now, the points A, B, C, T will be coplanar if the vectors vector AB, vector AC and vector AD are coplanar and they will be coplanar if the scalar triple product of vector AB, vector AC and vector AD is equal to 0. So, let us find the scalar triple product now that will be the determinant 10 minus 12 minus 4 minus 6 10 minus 6 minus 4 to 10 that is equal to 10 into 100 plus 12, plus 12 into minus 60 minus 24 minus 4 into minus 12 plus 40 that comes out to be 1120 minus 1120 and that is equal to 0. Therefore, they are coplanar now 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.