 Hi, and welcome to the session. Let us discuss the following question. The question says, find the partition and vector equation of a line which passes through the point 1, 2, 3, and the spiler to the line minus x minus 2 divided by 1 equals to y plus 3 by 7 equals to 2z minus 6 divided by 3. Now begin with the solution. Given equation is minus x minus 2 by 1 equals to y plus 3 by 7 equals to 2z minus 6 by 3. Let's name this equation as equation number 1. Now 1 can be written as minus x minus 2 by 1 equals to y plus 3 by 7 equals to z minus 6 by 2 divided by 3 by 2. This implies x minus 2 by 1 equals to y plus 3 by 7 equals to z minus 3 by 3 by 2. Now here we will have x plus 2 by minus 1. As we're taking minus 1 common from the numerator, we can write this expression as x plus 2 by minus 1. Our direction ratios of this line are minus 1, 7 and 3 by 2. Direction ratios underline proportional to minus 1, 7 and 3 by 2 equals to 1, 2, 3. It's direction ratios proportional to minus 1, 7 and 3 by 2. So equation of required line will be x minus 1 by minus 1, y minus 2 by 7, z minus 3 by 3 by 2. An equation of a line which is parallel to a given line and is passing through a given point is equals to vector a plus lambda times vector v. Now as the required line is passing through the point 1, 2, 3, therefore vector a will be equal to i cap plus 2 j cap plus 3 k cap. Direction ratios of required line are proportional to minus 1, 7 and 3 by 2. So vector v will be minus i cap plus 7 j cap plus 3 by 2 k cap. Equation of required line is minus 1 divided by minus 1 equals to y minus 2 divided by 7 equals to z minus 3 divided by 3 by 2. And vector equation of required line is equals to i cap plus 2 j cap plus 3 k cap plus lambda times minus i cap plus 7 j cap plus 3 by 2 k cap. So this is our required answer. So this completes the session by NJK.