Vectors in Space (Calculus)?

Question

Find two unit vectors that make an angle of 60 degrees with v = <3,4>.

Thanks.

Answer 1

let &lt;a, b&gt; be the vector

so we know that a^2 + b^2 = 1

and now

cos 60° = &lt;a, b&gt; · &lt;3/5 , 4/5&gt;

1/2 = 3a/5 + 4b/5

5 = 6a + 8b

6a = 5 - 8b

[we also know that 36a^2 + 26b^2 = 36 .. . . from the above property of a unit vector]

thus

36a^2 = (5 - 8b)^2 = 36 - 36b^2

25 - 80b + 64b^2 = 36 - 36b^2

100b^2 - 80b - 11 = 0

b = (4 ± 3√3)/10

a = (5 - 8b)/6

since there are two values of b, then you have your vectors &lt;a, b&gt;

simple extract them.