1. Find a. A unit vector that is parallel to (1, 2, 3) b. A vector that points in the same direction as the vector (1, 2, 3) but has a magnitude of 5. 2. Mark each of the following statements as True (T) or False (F) a. The zero vector 0 (with magnitude |0| = 0 ) is perpendicular to all other vectors b. Any plane has only two distinct normal vectors c. Parallel planes share a same normal vector. (1. Parallel planes share a same normal vector. 3. Which of the following is a point in the plane parallel to 3x+4y2z = 6 containing the origin? a. (1,1,1) b. (1,2,3) c. (3,2,1) d. none of the above 4. Find a vector normal to the plane a. z: 3x+2y+42 b. containing the vectors u 2 4i j + 2k and v = i + 5j + 3k. 5. Find an equation of the plane with normal vector i + j + k containing the point (1, 2, 3) 6. Consider the points: A(0,0,0), B(1,2,3) and C(6,5,4). a. Determine whether the angle ABC is right, acute or obtuse. b. Find all unit vectors that are perpendicular to the plane that con- tains these three points. c. Find the area of the triangle with these three points as its vertices. 7. Consider the planes :L' + 2y + z = 1 and a: + y + z = 0. They intersect along a straight line. Determine a vector equation for their intersection. 8. Consider the plane 33: I 2y 42 = 3 and the straight line with equation r(t) = (215 + 5, 3t 5, 4t 6). a. Determine whether the line and the plane intersect. If they do, then nd their point of intersection b. Determine whether the point (0, 1, 3) belongs to the plane or not. c. Determine whether the point (3, 2, 1) belongs to the line or not. (1. Determine whether the given line intersects with the line with equa tion 1(t) 2 (3t + 4, 8t, 3t 7). 9. Consider the line with vector equation r(t) 2 (513 | 7, 2 15,1213 + 4) and the point (5,2, 9). a. Find the equation of the plane that contains both the given line and the given point. b. Find the equation of the plane that contains the given point and is perpendicular to the given line