Question Type 2: Given 2 vectors, classifying what type of lines they are Exercises

Classify the relationship between the lines $L_1$ and $L_2$ defined by:

$L_1: \boldsymbol{r} = \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix} + t \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}$

$L_2: \boldsymbol{r} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix} + s \begin{pmatrix} 1 \\ 2 \\ 4 \end{pmatrix}$

Classify the relationship between the lines $L_1: \bigl(1,1,1\bigr)+t\,(3,6,9)$ and $L_2: \bigl(4,7,10\bigr)+s\,(1,2,3)$.

Classify the relationship between the lines $L_1$ and $L_2$ defined by: $L_1: \mathbf{r} = \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix} + t \begin{pmatrix} 2 \\ -1 \\ 3 \end{pmatrix}$ $L_2: \mathbf{r} = \begin{pmatrix} 3 \\ 0 \\ 4 \end{pmatrix} + s \begin{pmatrix} -1 \\ 2 \\ -2 \end{pmatrix}$

Classify the relationship between the lines $L_1$ and $L_2$ defined by:

$L_1: \mathbf{r} = \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix} + t \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix}$

$L_2: \mathbf{r} = \begin{pmatrix} 0 \\ 1 \\ 1 \end{pmatrix} + s \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix}$

Classify the relationship between the lines $L_1$ and $L_2$ defined by:

$L_1: \mathbf{r} = \begin{pmatrix} 2 \\ 1 \\ 0 \end{pmatrix} + t \begin{pmatrix} 4 \\ 2 \\ 0 \end{pmatrix}$

$L_2: \mathbf{r} = \begin{pmatrix} 1 \\ 3 \\ 5 \end{pmatrix} + s \begin{pmatrix} 2 \\ 1 \\ 0 \end{pmatrix}$

Classify the relationship between the lines.

Classify the relationship between the lines $L_1$ and $L_2$ defined by: $L_1: \mathbf{r} = \begin{pmatrix} 2 \\ -1 \\ 3 \end{pmatrix} + t \begin{pmatrix} 4 \\ 2 \\ -6 \end{pmatrix}$ $L_2: \mathbf{r} = \begin{pmatrix} 6 \\ 1 \\ -3 \end{pmatrix} + s \begin{pmatrix} 2 \\ 1 \\ -3 \end{pmatrix}$

Classify the relationship between the lines $L_1$ and $L_2$ defined by:

$L_1: \mathbf{r} = \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix} + t \begin{pmatrix} 2 \\ 3 \\ 4 \end{pmatrix}$

$L_2: \mathbf{r} = \begin{pmatrix} 2 \\ 5 \\ 9 \end{pmatrix} + s \begin{pmatrix} 4 \\ 6 \\ 8 \end{pmatrix}$

Classify the relationship between the lines $L_1: \mathbf{r} = \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix} + t \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}$ and $L_2: \mathbf{r} = \begin{pmatrix} 5 \\ 0 \\ 3 \end{pmatrix} + s \begin{pmatrix} 4 \\ -1 \\ 2 \end{pmatrix}$.

Classify the relationship between the lines $L_1: \mathbf{r} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix} + t \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix}$ and $L_2: \mathbf{r} = \begin{pmatrix} 2 \\ 2 \\ 4 \end{pmatrix} + s \begin{pmatrix} 0 \\ 1 \\ -1 \end{pmatrix}$.

Classify the relationship between the lines $L_1$ and $L_2$ defined by: $L_1: \mathbf{r} = \begin{pmatrix} 3 \\ 0 \\ 1 \end{pmatrix} + t\begin{pmatrix} 1 \\ 1 \\ 2 \end{pmatrix}$ $L_2: \mathbf{r} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix} + s\begin{pmatrix} 2 \\ -1 \\ 1 \end{pmatrix}$

Classify the relationship between the lines $L_1$ and $L_2$ defined by:

$L_1: \mathbf{r} = \begin{pmatrix} 0 \\ 1 \\ 2 \end{pmatrix} + t \begin{pmatrix} 3 \\ -1 \\ 2 \end{pmatrix}$

$L_2: \mathbf{r} = \begin{pmatrix} 6 \\ -1 \\ 6 \end{pmatrix} + s \begin{pmatrix} 3 \\ -1 \\ 2 \end{pmatrix}$