 Hello and welcome to the session. Let's discuss the following question. It says, find the equation of the plane through the points 2, 2, minus 1 and 3, 4, 2 and the parallel to the line whose direction ratios are 7, 0 and 6. So let's now move on to the solution. Now the equation of the plane passing through the point 2, 2, minus 1 will be a into x minus 2 plus b into y minus 2 plus c into z plus 1 is equal to 0. Let us name this as 1. Also this plane passes through the point 3, 4, 2. Therefore this point satisfies the equation of the plane. So we have a into 3 minus 2 plus 4 into b into 4 minus 2 plus c into 2 plus 1 is equal to 0. So we have a plus 2 b plus 3 c is equal to 0. Let us name this as 2. Now we are given that this plane is parallel to the line whose direction ratios are 7, 0 and 6. So this is 1 is parallel to the line having direction ratios 7, 0 and 6. Therefore 7 into a plus 0 into b plus 6 into c is 0. That is 7 a plus 6 c is equal to 0. Let us name this as 3. Now we will solve equation 1 and 2 for a, b and c using method of cross multiplication. So cross multiplying 2 and 3 we have a upon 2 into 6 minus 0 into 3 is equal to b upon 7 into 3 minus 1 into 6 is equal to c upon 1 into 0 minus 7 into 2. So this is equal to a upon 12 minus 0 is equal to b upon 21 minus 6 is equal to c upon 0 minus 14. So we have a upon 12 is equal to b upon 15 is equal to c upon minus 14. Let this be equal to k. So this implies a is equal to 12 k, b is equal to 15 k, c is equal to minus 14 k. Now we put values of a, b, c in 1 we have 12 k into x minus 2 plus 15 k into y minus 2 minus 14 k into z plus 1 is equal to 0. Taking k common from the equation and dividing it by 0 we have 12 into x minus 2 plus 15 into y minus 2 minus 14 into z plus 1 is equal to 0. We have 12 x minus 24 plus 15 y minus 13 minus 14 z minus 14 is equal to 0. This implies 12 x plus 15 y minus 14 z minus 68 is equal to 0. And this is the required equation of the plane. Hence required equation of the plane is 12 x plus 15 y minus 14 z minus 68 is equal to 0. So this completes the question and the session. Why for now? Take care. Have a good day.