Posted by colt on .
Find two unit vectors that make an angle of 60° with
v =
3, 4
(Enter your answer as a commaseparated list of vectors. Round your answers to four decimal places.)

calculus 
Reiny,
Let's pick an arbitrary value for the first component, say 1.
then let the vector be (1,b)
(1,b)∙(3,4) = (1,b)(3,4)cos60°
3 + 4b = √(1+b^2)(5)(1/2)
6 + 8b = 5√(1+b^2)
36 + 96b + 64b^2 = 25(1+b^2) after squaring both sides
39b^2 + 96b + 11 = 0
Using the quadratic equation, I got
b = .1205 or b = 2.3411
so one vector is (1,.1205 , the other is (1, 2.3411)
however, when I sketched it, I noticed the second vector would make an angle of 120° , which is the supplement of 60°, so let's us
(1, 2.3411)
also you needed unit vectors:
(1, .1205)} = 1.00723 , so we have (1/1.00723)times vector(1..1205)
so one vector is (.9928,  .1196)
in the same way, find the unit vector for (1,2.3411)
I will check my first vector:
LS = (3,4)∙(.9928, .1196) = 2.5
RS = (.9928, .1196) (3,4)cos60°
= 1(5)(1/2) = 2.5
My first vector works!