Find 2 Unit Vectors at 60 Degrees with <3,4> - Dot Product Calculation

[nameVoid]

Find 2 unit vectors that make a 60 degree angle with <3,4>

Vector <a,b>
Taking b=1 cos60=1/2

3a+4=(5/2 )sqrt(a^2+1)

36a^2+96a+64=25a^2+25
11a^2+96a=-39
(sqrt(11)a+48)^2= 2265
+- a=(sqrt(2265)-48)/sqrt(11)

 

[Curious3141]

Find 2 unit vectors that make a 60 degree angle with <3,4>

Vector <a,b>
Taking b=1 cos60=1/2

3a+4=(5/2 )sqrt(a^2+1)

36a^2+96a+64=25a^2+25
11a^2+96a=-39
(sqrt(11)a+48)^2= 2265
+- a=(sqrt(2265)-48)/sqrt(11)

I don't see a question here.

But let me preempt it with a question of my own. You're asked to find unit vectors. Can you think of another condition you can impose on a and b to meet this requirement?

It's fine to do it the way you did (letting b = 1), but then you still have to find unit vectors in those directions. More work.