IB Mathematics Analysis and Approaches Question Type 3: Rewriting a Line from One Form Into Another Exercises

Rewrite the line given by the vector equation $\mathbf{r}=\left(\begin{array}{c}-2\\ -2\\ -2\end{array}\right)+t\left(\begin{array}{c}1\\ 3\\ 4\end{array}\right)$ 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 $$\mathbf{r}=\left(\begin{array}{c}0\\ 1\\ 6\end{array}\right)+k\left(\begin{array}{c}4\\ 2\\ 1\end{array}\right)$$

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 $$\mathbf{r}=\left(\begin{array}{c}4\\ -1\\ 3\end{array}\right)+k\left(\begin{array}{c}-2\\ 3\\ 0\end{array}\right)$$ in Cartesian form.

Rewrite the line given by the vector equation $$\mathbf{r}=\left(\begin{array}{c}0\\ 0\\ 0\end{array}\right)+\lambda \left(\begin{array}{c}1\\ -2\\ 3\end{array}\right)$$ in Cartesian form.

Rewrite the line given by the vector equation $$\mathbf{r}=\left(\begin{array}{c}5\\ 0\\ 0\end{array}\right)+u\left(\begin{array}{c}-1\\ 2\\ 1\end{array}\right)$$ in Cartesian form.

Rewrite the line given by the vector equation $$\mathbf{r}=\left(\begin{array}{c}-1\\ 4\\ 2\end{array}\right)+s\left(\begin{array}{c}2\\ -1\\ 3\end{array}\right)$$ in Cartesian form.

Express the line given by the vector equation $$\mathbf{r}=\left(\begin{array}{c}2\\ -3\\ 5\end{array}\right)+\lambda \left(\begin{array}{c}3\\ 0\\ -2\end{array}\right)$$ in Cartesian form.

Find the Cartesian equation of the line given by the vector equation $\mathbf{r}=\left(\begin{array}{c}1\\ 2\\ 3\end{array}\right)+t\left(\begin{array}{c}4\\ 5\\ 6\end{array}\right)$.

Rewrite the line given by the vector equation $$\mathbf{r}=\left(\begin{array}{c}3\\ 3\\ 0\end{array}\right)+k\left(\begin{array}{c}0\\ 4\\ 1\end{array}\right)$$ in Cartesian form.

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