(a) Find parametric equations for the line through (3, 1, 8) that is perpendicular to the plane x − y + 4z = 7. (Use the parameter t.) (x(t), y(t), z(t)) = (b) In what points does this line intersect the coordinate planes? xy-plane (x, y, z) = yz-plane (x, y, z) = xz-plane (x, y, z) =

Answer: • (x, y, z) = (3+t, 1-t, 8+4t) . . . equation of the line • xy-intercept (1, 3, 0) • yz-intercept (0, 4, -4) • xz-intercept (4, 0, 12)Step-by-step explanation:The line's direction vector is given by the coordinates of the plane: (1, -1, 4). So, the parametric equations can be ... (x, y, z) = (3, 1, 8) + t(1, -1, 4) . . . . . parametric equation for the lineor (x, y, z) = (3+t, 1-t, 8+4t)__The various intercepts can be found by setting the respective variables to zero: xy-plane: z=0, so t=-2. (x, y, z) = (1, 3, 0) yz-plane: x=0, so t=-3. (x, y, z) = (0, 4, -4) xz-plane: y=0, so t=1. (x, y, z) = (4, 0, 12)