A

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 \(B = [-2,4,3]\).
\(C = [1,-2,3],\ D = [-2,-1,-2]\)
\(C = [6,1,-4],\ D = [3,2,1]\)
\(C = [-3,5,7],\ D = [-6,6,12]\)
\(C = [-3,8,14],\ D = [-6,9,19]\)

9000101001

Level: 
A
Determine whether two lines $p$ and $q$ are identical, parallel, intersecting or skew. \[\begin{aligned} p\colon x & = 1 + t, & & \\y & = 2 - t, & & \\z & = 1 - t,\ t\in \mathbb{R} & & \end{aligned}\] \[\begin{aligned} q\colon x & = 2s, & & \\y & = -1, & & \\z & = 2 - 2s,\ s\in \mathbb{R} & & \end{aligned}\]
intersecting lines
skew lines
identical lines
parallel lines, not identical

9000101002

Level: 
A
Find the intersection of the line \(AB\) and the line \(p\), where \(A = [0,1,2]\), \(B = [4,1,-2]\) and \[ \begin{aligned}p\colon x& = 1 + t, & \\y & = 2 - t, \\z & = 1 - t,\ t\in \mathbb{R}. \\ \end{aligned} \]
\([2,1,0]\)
\([1,2,1]\)
\([3,0,-1]\)
There is no intersection.

9000101003

Level: 
A
Find the value of the real parameter \(m\in \mathbb{R}\) which ensures that the lines \(p\) and \(q\) are parallel and not identical. \[ \begin{aligned}p\colon x& = 1 + t, & \\y & = 2 - t, \\z & = 1 - t,\ t\in \mathbb{R} \\ \end{aligned}\qquad \qquad \begin{aligned}q\colon x& = s, & \\y & = -s, \\z & = 3 + ms,\ s\in \mathbb{R}. \\ \end{aligned} \]
\(m = -1\)
\(m = -2\)
\(m = 0\)
\(m = 1\)