Question
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Consider the three displacement vectors A rightarow = (3^i - 3^j) m, B rightarow = (i^ - 4^j) m, and C rightarow = (-2i^ + 5^j) m. Use the component method to determine (a) the magnitude and direction of D rightarow = A rightarow + B rightarow + C rightarow and (b) the magnitude and direction of E rightarow = - A rightarow - B rightarow + C rightarow. Vector A rightarow has x and y components of -8.70 cm and 15.0 cm, respectively; vector B has x and y components of 13.2 cm and -6.60 cm, respectively. If A rightarow-B rightarow+3C rightarow=0, what are the components of C rightarow ? Given the vectors Arightarow= 2.00i^ + 6.00j^ and _B = 3.00 i^- 2.00j^, (a) draw the vector sum C rightarow = Arightarow + Brightarow and the vector difference D rightarow = A rightarow - B rightarow. (b) Calculate C rightarow and D rightarow, in terms of unit vectors, (c) Calculate C rightarow and Drightarow in terms of polar coordinates, with angles measured with respect to the positive x axis.
Explanation / Answer
31) D = A+B+C = 3i -3j + i - 4j - 2i + 5j = 2i - 2j
magnitude = sqrt(2^2+2^2) = 2.83 m
direction = tan^-1(2/2 ) = 45 degrees
b) E = -A-B+C = -3i + 3j - i + 4j - 2i + 5j = -6i - 9j
magnitude = sqrt(6^2+9^2) = 9.23 m
direction = tan^-1(-9/-6 ) = 56.3degrees with -Xaxis or +236.3 with +x axis