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Solutions4

# Solutions4 - MATH 214 A1 Assignment 4 Due Friday June 3...

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MATH 214 A1 - Assignment 4 Due Friday, June 3, 5:00pm (1) Use inequalities to describe the solid cube in the first octant bounded by the coordinate planes and the planes x = 2 , y = 2 and z = 2. (2 marks) { ( x, y, z ) | 0 x 2 , 0 y 2 , 0 z 2 } (2) Write the following vectors as a product of their length and direction: (2 marks each) (a) h 9 , - 2 , 6 i 11 · h 9 11 , - 2 11 , 6 11 i (b) h 1 3 , 1 3 , 1 3 i 1 · h 1 3 , 1 3 , 1 3 i (c) h 1 , - 1 , 1 i 3 h 1 3 , - 1 3 , 1 3 i (3) Write down the equation for the four planes that bound the tetrahedron with corners (1 , 0 , 0) , (0 , 1 , 0) , (0 , 0 , 1) and (0 , 0 , 0). (4 marks) x = 0, y = 0, z = 0 and x + y + z = 1 (4) Show that for any vector v , the projection of v onto v is v . (3 marks) v · v | v || v | · v = | v | 2 | v || v | · v = 1 · v = v (5) Consider a sailboat being moved by the wind. If the wind exerts a force of 100 N due north and the boat travels at an angle 60 0 north of east, how much work is done by the wind in moving the boat 1 km. (3 marks) If the force is pointed in the direction of due north and the motion is in the direction 60 0

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Solutions4 - MATH 214 A1 Assignment 4 Due Friday June 3...

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