Consider the three displacement vectors A = ( 4i - 3j) m, B = (6i - 3j) m, and C

Question

Consider the three displacement vectors A = ( 4i - 3j) m, B = (6i - 3j) m, and C = (-6i + 5j) m. Use the component method to determine the following. (Take the +x direction to be to the right.) the magnitude and direction of the vector D = A + B + C magnitude Note that all three vectors lie in the xy plane so the sum of these vectors will also lie in the xy plane, direction The angle you give does not put the sum into the correct quadrant.0 counterclockwise from the +x axis the magnitude and direction of E = -A - B + C magnitude counterclockwise from the +x axis direction

Explanation / Answer

given,

A = (4i - 3j) m

B = (6i - 3j) m

C = (-6i + 5j) m

A + B + C = (4 + 6 - 6)i + (-3 - 3 + 5)j

A + B + C = 4i - 1j

magnitude = sqrt(4^1 + 1^2)

magnitude = 2.236 m

direction = 360 - tan^-1(1/4)

direction = 345.96 degree counterclockwise from x axis

for E

E = -A - B + C

-A - B + C = (-4 - 6 - 6)i + (3 + 3 + 5)j

-A - B + C = -14i + 11j

magnitude = sqrt(14^2 + 11^2)

magnitude = 17.8 m

direction = 180 - tan^-1(11/14)

direction = 141.84 degree counter clockwise from x axis

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