Question Type 3: Rewriting a line from one form into another Exercises

Rewrite the line given by the vector equation $\mathbf{r} = \begin{pmatrix} -2 \\ -2 \\ -2 \end{pmatrix} + t \begin{pmatrix} 1 \\ 3 \\ 4 \end{pmatrix}$ in Cartesian form.

Rewrite the line given by the vector equation $\mathbf{r}=(7,2,-5)+t(3,-6,9)$ in cartesian form.

Find the Cartesian equation of the line with vector equation $\mathbf{r}=\begin{pmatrix} 0 \\ 1 \\ 6 \end{pmatrix} + k \begin{pmatrix} 4 \\ 2 \\ 1 \end{pmatrix}$

Rewrite the line given by the vector equation $\mathbf{r}=(1,0,2)+s(0,0,1)$ in Cartesian form.

Rewrite the line given by the vector equation $\mathbf{r} = \begin{pmatrix} 4 \\ -1 \\ 3 \end{pmatrix} + k \begin{pmatrix} -2 \\ 3 \\ 0 \end{pmatrix}$ in Cartesian form.

Rewrite the line given by the vector equation $\mathbf{r} = \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix} + \lambda \begin{pmatrix} 1 \\ -2 \\ 3 \end{pmatrix}$ in Cartesian form.

Rewrite the line given by the vector equation $\mathbf{r}=\begin{pmatrix} 5 \\ 0 \\ 0 \end{pmatrix}+u\begin{pmatrix} -1 \\ 2 \\ 1 \end{pmatrix}$ in Cartesian form.

Rewrite the line given by the vector equation $\mathbf{r} = \begin{pmatrix} -1 \\ 4 \\ 2 \end{pmatrix} + s \begin{pmatrix} 2 \\ -1 \\ 3 \end{pmatrix}$ in Cartesian form.

Express the line given by the vector equation $\mathbf{r} = \begin{pmatrix} 2 \\ -3 \\ 5 \end{pmatrix} + \lambda \begin{pmatrix} 3 \\ 0 \\ -2 \end{pmatrix}$ in Cartesian form.

Find the Cartesian equation of the line given by the vector equation $\mathbf{r} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix} + t \begin{pmatrix} 4 \\ 5 \\ 6 \end{pmatrix}$.

Rewrite the line given by the vector equation $\mathbf{r} = \begin{pmatrix} 3 \\ 3 \\ 0 \end{pmatrix} + k \begin{pmatrix} 0 \\ 4 \\ 1 \end{pmatrix}$ in Cartesian form.

Rewrite the line given by the vector equation $\mathbf{r}=(-1,0,4)+t(2,2,2)$ in cartesian form.