Question

Find two unit vectors that make an angle of 45 with 4i+3j

Answer 1

we know that u and v are unit vectors , therefore, =1.

norm of u gets: x^2+y^2=1

norm of v gets: = 5.

u*v= norm of u*norm of v(cos (Pi/4))

(xi+yj)*(4i+3y)=5(1/radical (2))

x=5/4radical(2)-3/4y

then I just solve for x, from norm of u, and solve for y then. then I will have answer with 2 unit vectors. I am wondering if there is any easier way to do this problem because the algebra is a bit intensive, ty.