 Hello, I am welcome to the session. I am Deepika here. Let's discuss the question which says find the vector and Cartesian equations of the plane that passes through the point 146 and the normal vector to the plane is i cap minus 2j cap plus k cap. Now we know that the equation of a plane through a point whose position vector is a and perpendicular to the vector and is vector r minus vector a into vector m is equal to 0. So this is the vector equation of the plane. Again the equation of a plane perpendicular to a given line with direction ratios a, b, c and passing through a given point x1, y1, z1 is a into x minus x1 plus d into y minus y1 plus c into z minus z1 is equal to 0. So this is the Cartesian equation of the plane. So this is the key idea behind our question. We will take the help of this key idea to solve the above question. So let's start the solution. Let the plane passes through a point a with coordinates 146 with position vector a and perpendicular to the vector n. We have vector a as i cap plus 4j cap plus 6k cap and vector n is given to us which is i cap minus 2j cap plus k cap. Therefore the vector equation of the plane is given by vector r minus vector a into vector n is equal to 0 or vector r minus vector a which is i cap plus 4j cap plus 6k cap into vector n which is i cap minus 2j cap plus k cap is equal to 0. So this is a vector equation of the plane. Now the Cartesian equation of the plane is given by 2x minus x1 plus b into y minus y1 plus c into z minus z1 is equal to 0. Here we have a is equal to 1, b is equal to minus 2, c is equal to 1 and the point x1, y1, z1 is the point 146. So we have the Cartesian equation of the plane as 1 into x minus 1 minus 2 into y minus 4 plus 1 into z minus 6 is equal to 0 or x minus 1 minus 2y plus a plus z minus 6 is equal to 0 or x minus 2y plus z plus 1 is equal to 0. So this is a Cartesian equation of the plane which passes through the point 146 and whose normal vector to the plane is i cap minus 2j cap plus k cap. Hence the answer for the above question is vector equation is given by vector r minus i cap plus 4j cap plus 6k cap into i cap minus 2j cap plus k cap is equal to 0 and the Cartesian equation of the plane is given by x minus 2y plus z plus 1 is equal to 0. So this completes our session. I hope the solution is clear to you. Bye and take care.