Analytical Plane Geometry

9000107501

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

9000107505

Level: 
B
Find \(\cos \varphi \) where \(\varphi \) is the angle between the lines \(p\) and \(q\). \[ \begin{aligned}[t] p\colon x& = 1 + 4t, & \\y & = 3 - 3t,\ t\in \mathbb{R}, \\ \end{aligned} \quad q\colon x + y - 3 = 0 \]
\(\frac{7\sqrt{2}} {10} \)
\(- \frac{7} {5\sqrt{2}}\)
\(\frac{\sqrt{2}} {5} \)
\(\frac{\sqrt{2}} {10} \)

9000106002

Level: 
A
In the following list identify a vector in the direction of the following parametric line. \[\begin{aligned} x =\ &t - 1, & & \\y =\ &t - 2,\ t\in \mathbb{R}\text{.} & & \end{aligned}\]
\(\left (1,1\right )\)
\(\left (1,2\right )\)
\(\left (-1,-2\right )\)
\(\left (1,-1\right )\)