Consider the three displacement vectors A vector = (-4i - 3j) m, B vector = (5i

Question

Consider the three displacement vectors A vector = (-4i - 3j) m, B vector = (5i - 7j) m, and C vector = (-8i + 5j) m. Use the component method to determine the following. (Take the +x direction to be to the right.) (a) the magnitude and direction of the vector D vector = A vector + B vector + C vector magnitude m direction degree counterclockwise from the +x axis (b) the magnitude and direction of E vector = -A vector - B vector + C vector magnitude m direction degree counterclockwise from the +x axis

Explanation / Answer

Given :-

A = (-4i - 3j)m

B = (5i - 7j)m

C = (-8i + 5j)m

a)

D = A + B + C

D = (-4i - 3j)m + (5i - 7j)m + (-8i + 5j)m

D = (-7i - 5j)

IDI = sqrt(7^2 + 5^2)

IDI = 8.6 m

theta = tan^-1(5/7) = 35.5 degree

b)

D = - A - B + C

D = -(-4i - 3j)m - (5i - 7j)m + (-8i + 5j)m

D = (-9i + 15j)

IDI = sqrt(9^2 + 15^2)

IDI = 17.5 m

theta = tan^-1(15/9) = 59 degree

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