A

9000101007

Level: 
A
Find the value of the real parameter \(m\) which ensures that the following two lines are identical. \[ \begin{aligned}p\colon x& = 1 + t, & \\y & = 2 - t, \\z & = 1 - t;\ t\in \mathbb{R} \\ \end{aligned}\qquad \qquad \begin{aligned}q\colon x& = s, & \\y & = 1 + s, \\z & = 3 + ms;\ s\in \mathbb{R} \\ \end{aligned} \]
No solution exists.
The lines are identical for every real \(m\).
\(m = -2\)
\(m = 2\)

9000101009

Level: 
A
Determine whether the following two lines are identical, parallel, intersecting or skew. \[\begin{aligned} a\colon x & = t, & & \\y & = -t, & & \\z & = 1 - t;\ t\in \mathbb{R} & & \end{aligned}\]\[\begin{aligned} b\colon x & = -s, & & \\y & = s, & & \\z & = 1 + s;\ s\in \mathbb{R} & & \end{aligned}\]
identical lines
skew lines
intersecting lines
parallel, not identical lines

9000101010

Level: 
A
Determine whether the following two lines are identical, parallel, intersecting or skew. \[\begin{aligned} a\colon x & = t, & & \\y & = -t, & & \\z & = 1 - t;\ t\in \mathbb{R} & & \end{aligned}\]\[\begin{aligned} b\colon x & = -s, & & \\y & = s, & & \\z & = -1 + s;\ s\in \mathbb{R} & & \end{aligned}\]
parallel, not identical lines
skew lines
intersecting lines
identical lines

9000100710

Level: 
A
Given points \(A = [-3;2]\) and \(B = [1;y]\), find the values of \(y\) which ensure the length of the vector \(\overrightarrow{AB } \) equals \(5\).
\(y_{1} = -1\), \(y_{2} = 5\)
\(y_{1} = -1\), \(y_{2} = 1\)
\(y_{1} = 1\), \(y_{2} = 5\)
\(y_{1} = 5\), \(y_{2} = -5\)

9000101803

Level: 
A
In the following list identify a pair of points \(C\), \(D\) such that the vector \(\overrightarrow{CD } \) is not equal to the vector \(\overrightarrow{AB } \) where \(A = [1;3;-2]\) and \(B = [-2;4;3]\).
\(C = [1;-2;3],\ D = [-2;-1;-2]\)
\(C = [6;1;-4],\ D = [3;2;1]\)
\(C = [-3;5;7],\ D = [-6;6;12]\)
\(C = [-3;8;14],\ D = [-6;9;19]\)