Given the vectors A vector = 2.00 i^+ 4.00 j^and B vector = 3.00 i^- 4.00 j^. (a

Question

Given the vectors A vector = 2.00 i^+ 4.00 j^and B vector = 3.00 i^- 4.00 j^. (a) Draw the vector sum c vector = A vector + B vector and the vector difference D vector = A vector - B vector. (Do this on paper. Your instructor may ask you to turn the paper in.) (b) Calculate C vector and D vector in terms of unit vectors. C vector = i^+ j^ D vector = i^+ j^ Calculate C vector and D vector in terms of polar coordinates, with angles measured with respect to the +x axis. vector C vector r = Theta = vector D vector r = theta =

Explanation / Answer

GIven,

A = 2 i + 4 j ; B = 3i - 4 j

a)

b)C = A + B

C = 2 i + 4 j + 3i - 4 j = 5 i - 0 j

Hence, C = 5 i - 0 j

D = 2 i + 4 j - 3i + 4 j = - 1 i - 8 j

Hence, D = -1 i - 8 j

C = sqrt (5^2 + 0^2) = 5

Hence, C = 5

theta = tan^-1(5/0) = 0

Hence, theta-c = 0

D = sqrt (1^2 + 8^2) = 8.06

theta = tan^-1(-8/-1) = 82.87 deg

Hence, theta-d = 82.87 deg

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