Please show work on paper with step by step solution for full points. thank you.

Question

Please show work on paper with step by step solution for full points. thank you.

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

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