 Hi and welcome to the session. My name is Mansi and I'm going to help you with the following question. The question says the dot product of a vector with the vectors i cap plus j cap plus 3k cap, i cap plus 3k cap minus 2k cap and 2i cap plus j cap plus 4k cap are 0, 5 and 8 respectively find the vector. Let us see the solution to this question. First of all let the required vector be x i cap plus y j cap plus z k plus y j cap i cap plus j cap is equal to 0. This implies x plus y minus 3 z is equal to 0. We call this equation 1. Similarly, plus y j cap plus z k cap minus 2 k cap is equal to 5. This implies x plus 3 y minus 2 z is equal to 0 and we call this equation 2 again plus y j cap plus z k cap into this implies 8 and we call this equation 3. Now solving 1, 2 and 3 for x, y and z to 1, y is plus 2 j cap plus k cap. This is also our answer to this question. I hope that you understood the solution and enjoyed the session. Have a good day.