Asked by sam
Find two unit vectors that make an angle of 60° with
v =
<6, 8>
v =
<6, 8>
Answers
Answered by
Damon
sketch it first
angle from x axis = tan^-1 (8/6) = 53.1 deg
so first clockwise 60 degrees
so -6.87 degrees (in quadrant 4)
tan -6.67 = -.12
so if x = 1, y = -.12
now we want that to be a unit vector so find magnitude of what we have
r = sqrt(x^2 + y^2)
= sqrt 1.014 = 1.007
so
< 1/1.007 , -.12/1.007 >
now you can do the 60 degrees counterclockwise from 53.1 which will be in quadrant 2, x negative, y positive
angle from x axis = tan^-1 (8/6) = 53.1 deg
so first clockwise 60 degrees
so -6.87 degrees (in quadrant 4)
tan -6.67 = -.12
so if x = 1, y = -.12
now we want that to be a unit vector so find magnitude of what we have
r = sqrt(x^2 + y^2)
= sqrt 1.014 = 1.007
so
< 1/1.007 , -.12/1.007 >
now you can do the 60 degrees counterclockwise from 53.1 which will be in quadrant 2, x negative, y positive
Answered by
sam
how do you do it without using a calculator?
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