Determine the acute angle between the vector $$x =(1, 2, -1),$$ and the plane containing the lines $$r:(5, 0, 0) + t(-1, 1, 2)$$ and $$s:(5, 0, 0) + u(3, 1, 1)$$
There is a lot going on here for me and I don't know what to do first. Do I find the normal? Use cross/dot product? Pointing me in the right direction is all I need..
Your direction vectors are $(-1, 1, 2)$ and $(3, 1, 1)$
Find the cross product of these vectors to get the normal vector to the plane.
Find the angle between the normal vector and $(1, 2, -1)$ using the dot product.
If the angle is not acute, subtract it from $\pi$
That is the desire angle.