5. Determine vector and parametric equations of the plane that... a) has the scalar equation 2x-y+ 3z-24 = 0 b) that contains two intersecting lines F (3,-1,2)+ s(4,0,1) and F=(3,-1,2)+(-2,1,5)

Consider the points P, Q and R with position vector (with respect to the origin O = (0,0, 0)) = (4, 1, –1), 6 = (2, 5, 0) and č= (-1,6,4). - (a) Compute the parametric and general (Cartesian) equation(s) of the line li that passes through P and Q. (b) Give an equation for the plane B determined by P, Q and R. (c) Compute the distance of the origin O to the plane 3 obtained in part (b).

Write the equation of the plane passing through P with direction vectors u and v in vector form and parametric form. P-AAK--[1]-[3] P = (0, 0, 0), u = , V = (a) vector form 3 1 0-0-0- = + s Z 3 + t (b) parametric form (Enter your answers as a comma-separated list of equations.)

Take the parametric equations of the lines [x/13 = y/3 = z/8] and [x-11/-10 = y-3/-4 = z-8/-7]; Find the scalar equation of the lines in the form of ax+by+cz+d=0  Show how to check that (13,3,8) fits the equation of the plane. Show how to check how (0,0,0) fits the equation of the plane. Show to to check that (1,-1,1) fits the equation of the plane.