 Hello students, let's work out the following problem. It says find the equation of the plane passing through the points 0-1, 0, 1, 1, 1, 3, 3, 0. So let's now move on to the solution. Now equation of the plane passing through the point x1, y1, z1, x2, y2, z2 and x3, y3, z3 is given by determinant of x-x1, y-y1, z-z1, x2-x1, y2-y1, z2-z1, x3-x1, y3-y1, z3-z1. So the equation of the plane passing through points 0-1, 0, 1, 1, 1 and 3, 3, 0 will be given by the determinant x-x1, x1 is 0, y-y1, y1 is minus 1, z-z1, z1 is 0, then x2-x1, x2 is 1, x1 is 0, y2-y1, y2 is 1, y1 is minus 1, z2-z1, z2 is 1, z1 is again 0, then x3-x1, x3 is 3, x1 is 0, then y3-y1, y3 is 3, y1 is minus 1, then z3-z1, that is 0 minus 0, this is z3. Now we will expand this determinant and before expanding we will simplify this little bit, x-0 is x, y-1 is y plus 1, z1-0 is 1, 1-1 is 1 plus 1, that is 2, 1-0 is 1, 3, 3-1 is 3 plus 1, that is 4, 0. Now we will expand this determinant along first row. So, we have x into 0 into 2 is 0 minus 4 into 1, that is 4 minus of y plus 1 into 0 into 1 is 0, 0 minus 3 into 1 plus z into 4 into 1 that is 4 minus 3 into 2 that is 6 and this determinant is equal to 0. So, this is equal to 0. So, now this is minus 4 into x is minus 4 x minus y plus 1 into minus 3 is plus 3 into y plus 1 plus z into minus 2 is equal to 0. This is again equal to minus 4 x plus 3 y plus 3 minus 2 z is equal to 0 and this implies minus 4 x plus 3 y minus 2 z plus 3 is equal to 0. Therefore, equation of the plane is minus 4 x plus 3 y minus 2 z plus 3 is equal to 0. So, this completes the question and the session. You just remember the Cartesian equation of the plane passing through the three points is given by this determinant. You need to remember this. So, this completes the session. Bye for now. Take care. Have a good day.