A

9000120303

Level: 
A
Identify a valid relation involving the angle \(\alpha \) defined as an angle between a solid diagonal and a face diagonal through the same vertex in a cube.
\(\mathop{\mathrm{tg}}\nolimits \alpha = \frac{\sqrt{2}} {2} \)
\(\sin \alpha = \frac{\sqrt{3}} {2} \)
\(\cos \alpha = \frac{\sqrt{5}} {3} \)
\(\mathop{\mathrm{cotg}}\nolimits \alpha = \sqrt{3}\)
\(\alpha = 45^{\circ }\)

9000107501

Level: 
A
In the following list identify a line which is perpendicular to the line \( 3x - 2y + 11 = 0\).
\(\begin{aligned}[t] x& = 3t, & \\y & = 1 - 2t,\ t\in \mathbb{R} \\ \end{aligned}\)
\(\begin{aligned}[t] x& = 1 + 2t, & \\y & = 2 - 3t,\ t\in \mathbb{R} \\ \end{aligned}\)
\(\begin{aligned}[t] x& = 2 - t, & \\y & = 3 + t,\ t\in \mathbb{R} \\ \end{aligned}\)
\(\begin{aligned}[t] x& = 2 + 3t, & \\y & = 1 + 2t,\ t\in \mathbb{R} \\ \end{aligned}\)