4. Consider the line l given by (x, y, z) = (2,1,3) + t(1, 2, 1), for some parameter t,
and the plane II given by 2x-4y+2z-1 = 0.
(a) Is the line l perpendicular to the plane II? Justify your answer.
(b) If l intersects the plane II, then find the point of intersection.
Do not forget to include all details of the solution. Answers without details worth
no points. No decimals or decimal approximations.
5. (a) Does the point P(2, 1, -1) lie on the line l given by the vector equation
(x, y, z) = (1, 1, -2) + t(1, 2, 1), for some parameter t? Justify your answer.
(b) If P does not lie on l, then find the equation of the plane II containing P and
l. Simplify your answer.
Do not forget to include all details of the solution. Answers without details worth
no points. No decimals or decimal approximations.
