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The following exercise adopt the notation {r, Theta}=r cos Theta i^+r sin Theta j^, where i^ and j^ are unit vector along the coordinate axes. Angles are in radians. Calculate each of the following vector sums, and express your answers in the form {r, Theta}. Feel free to draw diagrams to aid or illustrate your solutions. {1,0}+{0,0} {1,0}+{1,pi} {1,0}+{1,pi/2} {1,0}+{2,pi/2} {1,0}+{1,-pi/2} {2,pi/4}+{2,-pi/4} {3,pi/3}+{3,2pi/3} {3,pi/3}+{4,5pi/6} {r, alpha}+{r, beta} {a, alpha}+{b, beta}
Show transcribed image text The following exercise adopt the notation {r, Theta}=r cos Theta i^+r sin Theta j^, where i^ and j^ are unit vector along the coordinate axes. Angles are in radians. Calculate each of the following vector sums, and express your answers in the form {r, Theta}. Feel free to draw diagrams to aid or illustrate your solutions. {1,0}+{0,0} {1,0}+{1,pi} {1,0}+{1,pi/2} {1,0}+{2,pi/2} {1,0}+{1,-pi/2} {2,pi/4}+{2,-pi/4} {3,pi/3}+{3,2pi/3} {3,pi/3}+{4,5pi/6} {r, alpha}+{r, beta} {a, alpha}+{b, beta}