This is not a project and/or assignment for marks, as this is a textbook question, and will not be copying the tutors work. Do all the question in full solutions and details, and show all your work throughout out the questions, including formulas used. Write in full sentences needed and therefore statement as well. Answer all 7 questions.

1. The diagram shows a regular hexagon. Write a single vector that is equivalent to each vector expression. Illustrate this vector in the diagram. a) AE + EB = C b) AC - BC = d) DB - EA - DE = E D 2. If x = 2a - 3b - 46, y = -2a + 3b + 36, and Z = 2a - 3b - 56, determine the simplified expression for 2x - 3y + 52. 3. A (-3, 2, -5) and B (6, 7, 2) are two points in R3. Determine: a) |ABI b) A unit vector in the direction of BA 4. Find the components of the vector with the opposite direction to that of the vector from M(2,3,5) to M(8, 1,2).5. The vectors a, b, care shown. Construct your own vector using those 3 vectors. Your resultant vector must be of different magnitude (use some scalar values). a 6. Sketch the vector w on the grid on the right and label its coordinates. Vectors v and v + w are illustrated on the given Cartesian plane. (6, 4) -X 4 6 87. Tammy is golfing. She wants to drive her ball from the tee to the hole that lies due east. However, a gust of wind blows south and cause the ball to land 200 m away from the tee at E18'S. Her second shot is 82m and lands directly in the hole. The given vector diagram illustrates this information. If Tammy's first shot takes 3.25s to land, what is the magnitude of the velocity of the gust of wind blowing south? [5T] Hint: Determine the magnitude of the horizontal velocity, draw a vector diagram with the gust of wind, and solve. N Gust Hole Tee - E 180 200 m 82.0 m S