Help with calculus 3 question

how do i find the unit vector that will make the dot product of that unit vector and another vector equal to a certain number?

this is the problem:

<3,-4> · u = 4 , what is u?

where u is the unit vector.


there are two answers, u = <0,-1> and u = <24/25, -7/25>

i really would like to know how to get that answer, an explanation would really help me. thank you in advance.

I take Lizzy's answer a bit further
Let u = also x^2 +y^2 = 1...................1;
we have 3x - 4y = 4 ................................... 2
Substituting for y from 2 in 1 , we have
x^2 + {3/4)x -1}^2 = 1 or
x^2 + (9/16)*x^2 -(3/2)*x +1 = 1 or
(25/16)*x^2 - (3/2)*x = 0 or x{(25/16)x - (3/2)}
which means x = 0 or (16/25)*(3/2) = (24/25). So, using 1 u could be
<0,1>, <0,-1>, <24/25,7/25> and <24/25,-7/25>, out of these 4 values only
<0,-1> and <24/25,-7/25> give
<3,-4> · <0,-1> = 4; <3,-4> · <24/25,-7/25> = 4
So there are two solutions to the problem:
<0,-1> and <24/25,-7/25>.

"What is u?" It's "What ARE you?" You're grammatically incorrect.

P.S. I'm not actually serious. I just have no idea how to solve that problem. :)

well lets say u=

so dot product would be like 3(x)+(-4)y=4