Find Vectors to Make 60° Angle w/ v=<3,4>

[hazellaw]

how to find two vectors that make an angle of 60^O with v=<3,4>??

can i let b=<x,y>, then

cos60=(3x+4y)/5sqrt(x²+y²)

5sqrt(x²+y²)=3x+4y

 

[tiny-tim]

Welcome to PF!

Hi hazellaw! Welcome to PF!

(have a square-root: √ and a degree: º )

how to find two vectors that make an angle of 60^O with v=<3,4>??

can i let b=<x,y>, then

cos60=(3x+4y)/5sqrt(x²+y²)

5sqrt(x²+y²)=3x+4y

That'll certainly do it.

But easier would be

i] use <cosθ,sinθ> instead of <x.y>

or ii] write <3,4> in polar form (r,θ)

or iii] find the line perpendicular to <3,4>, and go along it the appropriate distance.