Answer Happy

3. Each of the following questions is worth 1 mark. State whether the following statements are true or false. Justify your answer. (a) Let S be a plane normal to a vector n. Let P and Q be points not on S. If n P = 0, then P and Qlie on the same side of S. (b) The distance between the z-axis and the line x - 1 = y = 0 is 1. (c) Any three distinct points A, B, C in R³ determine a unique plane. (d) The vector (1, 2, 3) is parallel to the plane 2x + 4y + 6z = 4. (e) Every vector lying on the line r = (1+2t, 1+3t, 1+4t) is parallel to the vector (1, 1, 1). (f) The line r = (1 + 2t, 1+ 2t, 1 – 4t) intersects the plane x+y+z=9 at a right angle. (g) The two planes x+y-z = 1 and -x-y +z = 2 intersect in a line.