A triangular prism has a base area of 30 square centimeters and a height of 10 centimeters. Calculate the volume of this triangular prism and then compare it to the volume of a triangular pyramid with the same base area and height.

Find the equation of the plane that passes through the point \( P(1,2,3) \) and has the normal vector \( \mathbf{N}=[2,-1,4] \).

If \( \triangle D E F \cong \angle B C A \), write the part that corresponds to: \( \begin{array}{ll}\text { (a) } \angle E & \text { (b) } \overline{E F} \\ \text { (c) } \angle F & \text { (d) } \overline{D F}\end{array} \)

Two lines \( \mathbf{r}_{1}(t)=[1+2 t, 3-t, 4+3 t] \) and \( \mathbf{r}_{2}(s)=[2+3 s, 1+s, 5-s] \) are:

Выяснить геометрический смысл соотношения \( \operatorname{Rez}=3 \)

Определите вид треугольника АВС, если А(6; 9), В(0; -8), С(4; -2). Тупоугольный Остроугольный Равнобедренный Прямоугольный