B

Find the distance between the points where the \(y\)-axis intersects the following hyperbola. \[ H\colon \frac{\left (x - 4\right )^{2}} {10} -\frac{\left (y - 5\right )^{2}} {15} = 1 \]

Consider a parallelogram \(ABCD\) with \(A = [1,3]\), \(B = [2,-1]\) and \(C = [5,1]\). Let \(S\) be the center of the diagonal \(BD\). Find the vector \(\overrightarrow{AS } \).

Find the angle between two lines and round your answer to the nearest minute. \[ \begin{aligned}p\colon x& = 2 - t , & \\y & = 3t , \\z & = 1 ,\ t\in \mathbb{R} \\ \end{aligned}\qquad \qquad \begin{aligned}q\colon x& = 2s, & \\y & = 4s , \\z & = 1 - s,\ s\in \mathbb{R} \\ \end{aligned} \]

Given points \(A = [0,1,2]\), \(B = [1,2,0]\), \(C = [1,2,3]\), find the angle between the lines \(AB\) and \(AC\). Round your answer to the nearest degree.