MCV4U 1. Consider the geometric vectors shown below: B D E a) Draw vector AB plus vector EF 0.5 marks A - correct interpretation 0.5 marks C - clear drawing b) Draw vector 1/2CD - 2FE 1 mark A - correct interpretation 1 mark C - clear drawing 2. Consider the vectors a= [1,3] and b=[2,-5]. a) Draw these as position vectors on a 2D Cartesian Plane 0.5 marks A - accuracy of sketch 0.5 marks C - clarity of sketch b) Determine the angles between these two vectors 2 marks, T - correct work performed 1 mark, K - correctness c) If vector a were translated such that it was colinear with the y-axis and pointing north,' give the quadrant bearing in this circumstance for vector b. 1 mark, A - correctness of quadrant bearing d) Find the distance between these two vectors (you can ignore the translation in 'c' to do this) 1 mark T - correct work performed 1 mark, K - correctness e) Solve 2b - 4a algebraically 1 mark T - correct approach 1 mark K - correctnessMCV4U 3. 3D Cartesian Vectors a) Use the right hand method to draw a 3D Cartesian Plane with three labeled axes. 0.5 marks A - correctness 0.5 marks C- clarity of sketch *Use the plane you have drawn above for part b b) Draw a vector with its tail at the origin and its head at point P (1,-6, 4) 0.5 marks A - correctness 0.5 marks C - clarity of sketch c) Determine the magnitude of this vector 1 mark K - correctness 4. Explain in two sentences of your own words, what a dot-product is and what a cross-product is. Then, give one real-life application of a dot-product, and one real-life application of a cross-product. 1 mark T - Correct understanding of dot and cross products 1 mark A - Correct real-world applications explained 1 mark C - Clarity and precision of explanation 5. Equations of a Line a) Write the vector equation for a line which goes through points A (1, 4) and B (3, 1) 1 mark, T - correct direction vector determined from slope 1 mark, K - correct final equation b) Determine one point which lies on this line: 1 mark, A - correct point c) Use parametric equations to determine if point (2, 3) is on the line and justify your reasoning 1 mark, K - correct equations employed 1 mark, T - correct conclusion is drawnMCV4U 6. Planes a) Explain what a plane is versus a line in your own words (one to two sentences) 1 mark, C - sound and clear explanation b) You have direction vectors: [3,1,2] and [-4,6,5] as well as a known point on the plane: (0,0,0). Determine a vector equation of this plane 1 mark, K - correct vector equation given c) Another plane has a normal vector (n) which is shown to be [-1,-2,-3]. We also know one known point on this plane is (3, 4, 5). Determine a scalar equation for this plane. 1 mark, T- correct procedure to determine equation 1 mark, C - correct scalar equation shown in proper form Total: 17K 18 T 16 A 16 C