Chapt. 3 Vectors and Trigonometry 33 c) Say that n is any number greater than 1. Find the numerical value of vector sum of the vectors v A = s i v A i and prove why it is that value. HINT: Imagine rotating the set of vectors by 360 ◦ /n . The sum vector should rotate too—but shouldn’t it also be in the same place as before? d) Now say that n = 1. The only vector in the set is v A 1 . What is the vector sum in this case? Why is it not the same in general as the vector sum found in the part (c) answer? 003 qfull 00790 3 5 0 tough thinking: vector rotational transformations Extra keywords: One needs a lot of hints for 20-minute test situation 6. Say you have a vector speci±ed by v r = ( x,y ) in relative to Cartesian x-y axes. Now create new x ′-y ′ axes by rotating the old axes by θ counterclockwise. The vector v r has NOT moved: it is still the same magnitude and physical direction. But relative to the new axes it is speci±ed by ( x
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