A farmer wants to fence off his four-sided plot of flat land. He measures the first three sides, shown as A, B, and C in the figure, and then correctly calculates the length and orientation of the fourth side D. What is his result?
We know that the sum of the 4 vectors is zero. So, Vector D is calculated as
We solve for the x-component first. The x-component of vector D is
We solve for the y-component.
Since we already know the x and y component of vector D, we can finally solve for the distance of vector D.
The corresponding direction of vector D is