6. A particle travels along the line r = 1 +t, y = 5 + 2t, = = -7 +t, where t is in seconds and r, y, z are in meters. (a) When and where does the particle hit the plane r + y + z = 1? (b) How fast is the particle going when it hits the plane? Give units. 7. The base of a 20-meter tower is at the origin. The base of a 20-meter tree is at (0, 20, 0). The ground is flat and the z-axis points upward. The following para- metric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (1) F(t) = (20 + (2) k (II) F(t) = 2127+ 212 K (III) F(t) = 207 + 20 3 + (20 -12) E (IV) F(t) = 2t j + (20-12) k (V) r(t) = (20 - 2t) i + 2t j + (20 - t) k (VI) " (t ) = tittitth (a) Which projectile is launched from the top of the tower and goes downward? When and where does it hit the ground? (b) Which projectile hits the top of the tree? When? From where is it launched? (c) Which projectile is not launched from somewhere on the tower and hits the tree? Where and when does it hit the tree