Chapter 11.3, Problem 47ES

For each x in $\left(-\infty ,+\infty \right),$ be the vector from the origin to the point $P\left(x,y\right)$ on the curve $y=x^2+1,$ the vector from the origin to the point $Q\left(x,y\right)$ on the line $y=-x-1.$

(a) Use a CAS to find, to the nearest degree, the minimum angle between $\text{u}\left(x\right)\text{ and v}\left(x\right)$ for x in $\left(-\infty ,+\infty \right).$

(b) Determine whether there are any real values of x for which $\text{u}\left(x\right)\text{ and v}\left(x\right)$ are orthogonal.