Final answer:
To find the equation of a plane going through points P, Q, and R, use the coordinates of the points to set up a system of equations and solve. To find the equation of a plane containing point P and perpendicular to vector QR, use the cross product. To find the vector equation of the intersection line of two planes, substitute one equation into the other and isolate a variable.
Step-by-step explanation:
To find the equation of the plane going through points P, Q, and R, we can use the formula for the equation of a plane: Ax + By + Cz = D. To find the values of A, B, C, and D, we can use the coordinates of the points. Plug in the coordinates of each point into the equation and set up a system of equations. Solve the system to find the values of A, B, C, and D.
To find an equation of a plane containing P and perpendicular to vector QR, we can use the cross product of the normal vector of the plane with QR. The normal vector of the plane is found by finding the cross product of the vectors formed by points P and Q, and P and R. Then, use the coordinates of P and the values of the normal vector to write the equation of the plane.
To find the vector equation of the line which is the intersection of the two planes, we can substitute the equation of one plane into the other, isolate a variable, and write the equation in vector form.