Vector addition is a matter of stringing together vectors in a head-to-tail fashion. It is a commutative property, meaning that the sum of vectors A and B equals that of B plus A. Therefore, illustrating vector addition results in a parallelogram, with the two instances of vector A forming two opposites sides, and those of vector B forming the other two. The sum is the parallelogram's diagonal which stretches from where the tails meet to where the heads meet. Finding the magnitude and direction is a fundamental task when working with vectors.
Instructions
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1
Find the x-component of the resultant vector by adding the x-components of the vectors being added. Do the same to find the y-component. For example, given the vectors (-1, -2) and (2, -1), the sum is (1, -3).
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2
Calculate the magnitude of the vector with the formula M = sqrt(x^2 + y^2), where M is the magnitude and x and y are the components of the resultant vector. For example, M = sqrt(1^2 + (-3)^2) = 3.16.
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3
Find the direction with the formula A = arctan(y/x), where A is the angle with respect to the x-axis. For example, A = artan(-3/1) = -71.6 degrees.