A

9000106608

Level: 
A
Determine whether the following two lines are identical, parallel, intersecting or skew. \[\begin{aligned} p\colon\, &x = 2, &q\colon\, &x =\phantom{ 1} - s, & & & & \\ &y = 2 + t, & &y = 4, & & & & \\ &z = 3;\ t\in \mathbb{R}, & &z = 1 - s;\ s\in \mathbb{R} & & & & \end{aligned}\]
intersecting lines
parallel lines, not identical
skew lines
identical lines

9000106201

Level: 
A
In the following list identify a vector having the same direction as the parametric line \(p\). \[ \begin{alignedat}{80} p\colon x & = 1 + 2t, & &\phantom{t\in \mathbb{R}} & & & & \\y & = 3 - 4t;\ & &t\in \mathbb{R} & & & & \\\end{alignedat}\]
\((1;-2)\)
\((1;3)\)
\((3;1)\)
\((2;3)\)

9000106609

Level: 
A
Determine whether two lines are identical, parallel, intersecting or skew. The first line is the line passes through the points \(A = [3;-2;1]\) and \(B = [0;7;7]\) and the second line is the line passes through the points \(C = [5;-8;-3]\) and \(D = [6;-11;-5]\).
identical lines
parallel lines, not identical
intersecting lines
skew lines

9000106610

Level: 
A
Determine whether two lines are identical, parallel, intersecting or skew. The first line is the line passes through the points \(A = [1;-4;2]\) and \(B = [3;0;0]\) and the second line is the line passes through the points \(C = [3;-5;5]\) and \(D = [-1;-3;-1]\).
intersecting lines
parallel lines, not identical
identical lines
skew lines