A

9000117406

Level: 
A
Determine whether the following planes are parallel, identical or intersecting. \[\begin{aligned} \rho \colon \frac{3} {2}x -\frac{1} {4}y + \frac{2} {3}z -\frac{2} {5} = 0,\qquad \sigma \colon \frac{2} {3}x - 4y + \frac{3} {2}z -\frac{5} {2} = 0 & & \end{aligned}\]
intersecting
identical
parallel, not identical

9000121004

Level: 
A
In the cube \(ABCDEFGH\) find the angle between the lines \(S_{AE}S_{HC}\) and \(S_{HC}S_{BF}\), where \(S_{AE}\), \(S_{HC}\) and \(S_{BF}\) are the centers of the segments \(AE\), \(HC\) and \(BF\), respectively.
\(53.13^{\circ }\)
\(26.57^{\circ }\)
\(60^{\circ }\)
\(36.87^{\circ }\)

9000120306

Level: 
A
The lengths of a side, face diagonal and solid diagonal through the vertex \(A\) in a rectangular box \(ABCDEFGH\) are \(|AB| = 6\, \mathrm{cm}\), \(|AC| = 10\, \mathrm{cm}\), \(|AG| = 15\, \mathrm{cm}\). Find the surface area.
\(\left (96 + 140\sqrt{5}\right )\, \mathrm{cm}^{2}\)
\(600\, \mathrm{cm}^{2}\)
\(236\sqrt{5}\, \mathrm{cm}^{2}\)
\(\left (48 + 70\sqrt{5}\right )\, \mathrm{cm}^{2}\)
\(240\sqrt{5}\, \mathrm{cm}^{2}\)

9000117403

Level: 
A
Determine whether the following planes \(\rho \) and \(\sigma \) are parallel, identical or intersecting. \[ \begin{aligned}[t] \rho \colon &x = -u + v, & \\&y = u + 2v, \\&z = -u - v;\ u,v\in \mathbb{R}, \\ \end{aligned}\qquad \sigma \colon x-2y-3z+1 = 0 \]
parallel, not identical
identical
intersecting