Consider the vectors A with arrow = 3.00 î + 5.00 and B with arrow = 4.00 î 3.00
ID: 1523366 • Letter: C
Question
Consider the vectors A with arrow = 3.00 î + 5.00 and B with arrow = 4.00 î 3.00 . Find the vector sum C with arrow = A with arrow + B with arrow and the vector difference D arrowbold = A with arrow B with arrow
(a) Calculate C with arrow and D arrowbold in terms of unit vectors. C with arrow = î + D arrowbold = î +
(b) Calculate C with arrow and D arrowbold in terms of polar coordinates, with angles measured with respect to the positive x axis. vector C with arrow magnitude direction ° counterclockwise from the +x axis vector D arrowbold magnitude direction ° counterclockwise from the +x axis
Please help with this question, thank you
Explanation / Answer
A+B = cA-B = D = -i + 8j
a) C' = C / |C| = (7i + 2j) / sqrt(53)
D' = D / |D| = (-i + 8j) / sqrt(65)
b) C = 7i + 2j
|C| = sqrt(53) = 7.28
theta = tan^-1(2/7) = 16 degg
C'' = 7.28(cos16 i + sin16 j)
D = -i + 8j
|D| = sqrt(65) = 8.06
theta = 180 - tan^-1(8/1) = 97.13 degg
D'' = 8.06(cos97.13 i + sin97.13 j)