ch03-p031 - 31. (a) As can be seen from Figure 3-32, the...

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(c) If the starting point is (0, a , 0) with the corresponding position vector ˆ j a , the diametrically opposite point is ( a , 0 , a ) with the position vector ˆˆ ik aa + . Thus, the vector along the line is the difference ˆ ij k a −+ . (d) If the starting point is ( a , a , 0) with the corresponding position vector i j + , the diametrically opposite point is (0, 0 , a ) with the position vector ˆ k a . Thus, the vector along the line is the difference ˆ k a −− + . (e) Consider the vector from the back lower left corner to the front upper right corner. It is ˆ j k . aaa ++ We may think of it as the sum of the vector a # i parallel to the x axis and the vector j k ## + perpendicular to the x axis. The tangent of the angle between the vector and the x axis is the perpendicular component divided by the parallel component. Since the magnitude of the perpendicular component is 22 2 a += and the magnitude of the parallel component is
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