Let m and n be two constants. Vectors in the form mi + nj can be represented as ordered pairs in the form (m,n). For the vector 6i-3j, it is located at (6,-3) since m = 6 and n = -3
Find the magnitude of the vector
r = magnitude
r = sqrt(m^2+n^2)
r = sqrt(6^2+(-3)^2)
r = sqrt(36+9)
r = sqrt(45)
r = 6.708 approximate
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Find the angle of the vector that it makes with the positive x axis.
theta = arctan(n/m)
theta = arctan(-3/6)
theta = arctan(-1/2)
theta = -26.565 degrees approximately
theta = -26.565+360
theta = 333.435 this is coterminal with the -26.565 degree angle
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The polar coordinates are approximately (r, theta) = (6.708, 333.435)
See the diagram below.
