Answer to Question #81099 in Classical Mechanics for Aygo

Question

Consider the three displacement vectors A with arrow = (2î − 3ĵ) m, B with arrow = (7î − 2ĵ) m, and C with arrow = (-3î + 1ĵ) m. Use the component method to determine the following.
(a) The magnitude and direction of the vector Darrowbold = A with arrow + B with arrow + C with arrow.
magnitude m
direction ° counterclockwise from the +x axis
(b) The magnitude and direction of E with arrow = −A with arrow − B with arrow + C with arrow.
magnitude m
direction ° counterclockwise from the +x axis

Answer 1

a+b+c=2î - 3ĵ+7î - 2ĵ-3î + 1ĵ=6î-4ĵ
√(6^2+4^2 )=7.2
θ=270+tan^(-1)⁡〖4/6〗=304

-a-b+c=-2î+ 3ĵ-7î+ 2ĵ-3î + 1ĵ=-12î+6ĵ
√(6^2+〖12〗^2 )=13.4
θ=90+tan^(-1)⁡〖6/12〗=117
(a) The magnitude and direction of the vector Darrowbold = A with arrow + B with arrow + C with arrow.
magnitude 7.2 m
direction 304° counterclockwise from the +x axis
(b) The magnitude and direction of E with arrow = −A with arrow − B with arrow + C with arrow.
magnitude 13.4 m
direction 117° counterclockwise from the +x axis