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Midterm 1 (w/ Solutions)

Midterm 1 (w/ Solutions) - Name Physics 121 Dr Callahan...

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Unformatted text preview: Name: Physics 121, Dr. Callahan Summer I 2008, Midterm #1 Solutions 1. Consider a room in the shape of a cube. A line is painted diagonally across the floor, from the southwest corner to the northeast. Another line is painted diagonally across the south wall, from the floor on the west side to the ceiling on the east. These lines meet at the bottom southwest corner. Find the angle that they make there. Answer: Put the origin at the bottom southwest corner. Let the x-axis point east, the y-axis point north and the z-axis point up. It doesn’t matter what the size of the cube is, so let’s say it’s a unit cube. Then the vector from the bottom southwest corner to the bottom northeast corner (diagonally across the floor) is a = ˆ ı + ˆ = (1 , 1 , 0). The vector from the bottom southwest corner to the top southeast corner (diagonally across the south wall) is b = ˆ ı + ˆ k = (1 , , 1). We want to find the angle between these vectors....
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Midterm 1 (w/ Solutions) - Name Physics 121 Dr Callahan...

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