Question

Problem 1. Perform the following vector operations both algebraically and graphically (if sensible) with the vectors A 4r +3ý, B-2y, and C which has magnitude 4 at 30° counterclockwise from the +r axis. Explain why your answer for each is a vector or a scalar: a. A B+C c. Find the magnitude and direction of A -

Answer 1

A^rightarrow = (4 x^+ 3y^) B^rightarrow = (x^+ 2y^) C^rightarrow = 4(30 degree = 4 cos (30 degree) x^+ 4 sin (30 degree) y^) = (3.464 x^+ 2y^) a. A^rightarrow + B^rightarrow + C^rightarrow = (4 x^+ 3y^) + (x^+ 2y^) + (3.464 x^+ 2y^) = (8.464 x^+ 7y^) b Vertical-bar 3B^rightarrow - c^rightarrow Vertical-bar = Vertical-bar 3(x^+ 2y^) - (3.464 x^+ 2y^) Vertical-bar = Vertical-bar -0.464 x^+ 4y^ Vertical-bar = squareroot (-0.464)^2 + (4)^2 = 4.0268 units c. A^rightarrow + C^rightarrow = (4 x^+ 3y^) + (3.464 x^+ 2y^) = (7.464 x^+ 5y^) magnitude, Vertical-bar A^rightarrow + C^righarrow Vertical-bar = squareroot (7.464)^2 + (5)^2 = 8.984 units direction theta = tan^-1 (5/7.464) = 33.817 degree (CCW from + x direction)