# Parametric equations x 9 7 s 8 t y 2 4 s t z 5 5 6 s

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9 ) Parametric equations: x = 9 7 s 8 t y = 2 4 s t z =− 5 + 5 6 s + 10 9 t 10. Given two vectors u =( 16,5,2 ) and v =( 3, 2, 2 ) , find the following: (6 marks: 3 marks each) a. The coordinates of the projection of u on v . u ∙v v ∙v proj v u = ¿ ) v ¿ ( ( 16 ) ( 3 ) + ( 5 ) ( 2 ) + ( 2 ) ( 2 ) ) ( ( 3 ) ( 3 ) + ( 2 ) ( 2 ) + ( 2 ) ( 2 ) ) ( 3, 2, 2 ) ¿ 54 17 ( 3, 2, 2 ) ¿ ( 162 17 , 108 17 , 108 17 ) b. The magnitude of the projection of u on v . ¿ proj v u ¿ ( 162 17 ) 2 + ( 108 17 ) 2 + ( 108 17 ) 2 ¿ 2916 17
Task 3: Communication questions 11. In your own words, describe the types of intersections that can be formed by two lines in 3-space. Define each type of intersection and provide a diagram for each. (8 marks: 2 marks each)
Skew: Lines that do not have the same direction and do not intersect. =(− 2,3,8 ) , verify the following arithmetic properties of vectors. (12 marks: 4 marks each) u