Textbook question about inner product and work. I have this questions from my textbook:

I don't understand this line:
$b = [-1, tan {25}] = [-1, 0.46631], thus |b| = 1.10338$
Where does the length b come from? How did 1.10338 come about? Why are we using tan 25? I don't understand the u line either.
 A: $b$ is a vector in the direction of the rope, it represents nothing in particular, and this vector's components are $(-1,\tan 25)$ (note that any vector in the direction of the rope must be a multiple of this one, so they took this one for simplicity)
And so the length of $b$ is $|b|=\sqrt{(-1)^2+ (\tan 25)^2}$
And how he got the components of $b$, in the right triangle (where the hypotenuse is the inclined plane that the car is on) we may suppose that the horizantal side of this triangle has a length of $1$ and $\tan 25=\frac{\text{opposite}}{\text{adjacent}}= \frac{\text{y-component of} \quad b}{1}$

To find the components of the vector of the direction of the rope you simply project it on the x-axis and y-axis
If the x-component was $-1$ then we calculate the y-component as above to find that it is $\tan 25$.
So $b=(-1,\tan 25)$
Note that during calculation of the y-component we used $1$ and not $-1$ because we are using the length which is always positive (and the $-$ actually is just for direction because it is opposite to the direction of the x axis)
