Applied Advanced Mathematics & Analysis question bank (Calculus, Vectors, Probability & Statistics)

$\frac{10}{\sqrt{6}}$ ($\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|} = \frac{2(1) + 3(2) + 2(1)}{\sqrt{1 + 4 + 1}}$) (3D Geometry: Direction Cosines, Direction Ratios, Planes and Lines in Space)

$\frac{{8}}{{\sqrt{{6}}}}$

$\frac{{10}}{{6}}$

$10\sqrt{{6}}$

$\frac{\pi}{4}$ (Using property $\int_0^a f(x)dx = \int_0^a f(a-x)dx \implies 2I = \frac{\pi}{2}$) (3D Geometry: Direction Cosines, Direction Ratios, Planes and Lines in Space)

$\frac{{\pi}}{{2}}$

$\frac{{\pi}}{{8}}$

$1$