| How do you convert the vector form \begin{pmatrix}7\\2\\3\end{pmatrix}=\lambda\begin{pmatrix}0\\5\\2\end{pmatrix} to cartesian form? | x=7, \frac{y-2}{5}=\frac{z-3}{2} |
| Find the cartesian equation of the line between (2,3,-2) and (5,8,5) | \frac{x-2}{3}=\frac{y-3}{5}=\frac{z+2}{7} |
| What is the direction vector \vec d for the line between (2,3,-2) and (5,8,5)? | \begin{pmatrix}3\\5\\7\end{pmatrix} |
| How do you express \lambda from x=2+3\lambda in the line between (2,3,-2) and (5,8,5)? | \lambda=\frac{x-2}{3} |
| How do you express \lambda from y=3+5\lambda in the line between (2,3,-2) and (5,8,5)? | \lambda=\frac{y-3}{5} |
| How do you express \lambda from z=-2+7\lambda in the line between (2,3,-2) and (5,8,5)? | \lambda=\frac{z+2}{7} |
| How do you find the direction vector for a line between two points (x_1,y_1,z_1) and (x_2,y_2,z_2)? | \vec d = \begin{pmatrix}x_2-x_1\\y_2-y_1\\z_2-z_1\end{pmatrix} |