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.
Parabola is a set of the points that are equidistant from the point (focus)
and the line (directrix). Find the equation of the directrix of the parabola
\(P\colon x^{2} - 4x - 6y - 17 = 0\).
Given points \(A = [-1,0,3]\),
\(B = [0,2,0]\), find the angle
between the line \(AB\)
and the line \(m\).
\[
\begin{aligned}m\colon x& = 1 + 2t, &
\\y & = -3t,
\\z & = 1,\ t\in \mathbb{R}
\\ \end{aligned}
\]
Round your answer to the nearest minute.
Parabola is a set of the points that are equidistant from the point (focus)
and the line (directrix). Find the equation of the directrix of the parabola
\(P\colon y^{2} + 4y + 4x - 4 = 0\).
Find the angle between the \(x\)-axis
and the line \(p\).
\[
\begin{aligned}p\colon x& = 2 - t, &
\\y & = 3t,
\\z & = 1,\ t\in \mathbb{R}
\\ \end{aligned}
\]
Round your answer to the nearest minute.
Parabola is a set of the points that are equidistant from the point (focus)
and the line (directrix). Find the equation of the directrix of the parabola
\(P\colon x^{2} - 8x + 6y + 19 = 0\).
The points \(A = [0,5,0]\),
\(B = [5,5,0]\),
\(C = [5,0,0]\),
\(D = [0,0,0]\) define the cube
\(ABCDEFGH\). Find the angle
between the lines \(BF\)
and \(AC\).
Round your answer to the nearest minute.