7. Line A goes through the points (4, 1, 0) and (1, 5, 2). Line B is parallel to line A and passes through the point (6, 1, 3). Find a parametrization for each of the lines. (Use a different variable for the two parameters.) 8. Line E goes through the points (1, 5, 2) and has the direction vector (2, 2, 3). Line F goes through the points (3, 1,6) and (5, 0,2). Do these lines intersect? If not, are they parallel? 9. [P] Particle 1 starts at point (3,1, 1) and particle 2 starts at point (10, 5, 4); at t = 0, both particles begin to move along linear paths. After 1 second, particle 1 is at point (4, 3, 4) and particle 2 is at (8, 6, 3). (a) Do the paths of the particles intersect? (b) Will the particles collide? 10. If v = (3, 2, 8) and w = {1, 6, k), then what values of k make an obtuse angle between v and w. 11. [P] Consider the triangle with vertices at (1,2,3), (1,2,5), and (0,6,3). (a) Is this triangle equilateral, isosceles, or scalene? (b) Is this triangle acute, right, or obtuse? 12. [P] A laser pointer is situated at the point (3, 1, 4) and is pointing a linear beam in the direction (1, 2, 2) towards the plane 450 y 52 = 7. On the plane is a target at the point (1, 12, 3). (a) Does the laser hit the target? If not, where does the laser hit the plane, and how far away is this from the target. (b) [G] How far off is the angle of the laser from hitting the target? Give your answer in degrees, rounded to 3 decimal places. 13. Are the following statements true or false? Explain why or why not. (a) A vector has only one unit vector parallel to it. (b) The same line /segment can have many different parametrizations. (c) The sphere $2 + y2 + Z2 = 1 is a threedimensional surface. ((1) If v and w are two vectors in R3, the magnitude of v + w is greater than both v and W