What is the angle between the two vectors $u = (1, 0, 1)$ and $v = (0, 1, 1)$ ?

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Evaluate the definite integral $\int_{0}^{1} x e^{x} d x$ .
Find the volume of the solid generated by revolving the region bounded by $y = x$ , $y = 0$ , and $x = 4$ about the x-axis.
Evaluate $\int \frac{2 x + 3}{x ^{2} + 3 x + 5} d x$ .
Find the center and radius of the sphere with equation $x^{2} + y^{2} + z^{2} - 4 x + 6 y - 2 z - 11 = 0$ .
Evaluate $\int_{0}^{π /2} sin^{3} x cos x d x$ .
What is the equation of the plane passing through the point $(1, 2, 3)$ with normal vector $n = (2, - 1, 4)$ ?