 Hello and welcome to the session. In this session we discuss the following question which says, find the Cartesian equation of the plane passing through the points A with coordinates 0, 0, 0 and B with coordinates 3 minus 1, 2 and parallel to the line x minus 4 upon 1 equal to y plus 3 upon minus 4 equal to z plus 1 upon 7. Before we move on to the solution, let's discuss first equation of the plane say a point A with coordinates x1, y1, z1 is given by A into x minus x1 plus B into y minus y1 B into z minus z1 is equal to 0. Where we have A, B and C are the direction ratios common to the plane. Let's discuss the condition when a line and a plane are parallel. Suppose we are given upon A1 equal to y minus y1 upon B1 is equal to z minus z1 upon C1. The equation of the plane is plus B to y plus C to z plus B is equal to 0 then this line is plus B1 B2 plus C1 C2 is equal to 0. This is the key idea that we use in this question. Let's now move on to the solution. We are given two points A and B so given the equation of a line you have to find the Cartesian equation of the plane which passes through these two points and is parallel to the given line. So we have a point A with coordinates 0, 0, 0 and a point B with coordinates 3 minus 1, 2. Now the equation of a plane that passes through A with coordinates 0, 0, 0 is given by x1 which is 0 plus B into y minus y1 which is 0 plus C into z minus z1 which is 0 is equal to 0. That is we have B y plus C z is equal to 0. Where again these A, B, C are the direction ratios normal to the plane. With this equation of the plane the equation 1 now next we have point B with coordinates 3 minus 1, 2 equation 2 we put 3 in place of y we put minus 1 in place of z we put 2. So we get minus B plus 2 C is equal to 0. Let this be equation given upon 1 is equal to y plus 3 upon minus 4 is equal to z plus 1 let this be equation 3. Also given that plane 1, 3, 0 using this condition we get minus 4 into B so minus 4 B 7 into 7 C is equal to 0. Now we have got two equations in the variables A, B and C. So we would solve the equations 2 and 4 and C solve these two equations by the cross multiplication method is equal to B upon 1 is equal to C upon 1 is equal to B upon minus 19 is equal to C upon minus 11 this be equal to some constant say lambda gives us A is equal to lambda minus 19 lambda C is equal to minus 11 lambda. Now equation 1 that is equation of the plane we get. So we put the values of A, B and C in this equation. So we now get lambda z is equal to 0 19 y minus 11 z is equal to 0. So this is the required equation of the plane. Hence the required equation of the plane is x minus 19 y minus 11 z is equal to 0. This is our final answer. This completes the session. Hope you understood the solution of this question.