Question

How do you find parametric equations and symmetric equations for the line through the points (1, 3, 2) and ( -4, 3, 0)?

Answer 1

Given two points `(x_1,y_1,z_1)` and `(x_2,y_2,z_2)` the standard form of the parametric equations of a line passing through both is:

`{(x=x_1+(x_2-x_1)t),(y=y_1+(y_2-y_1)t),(z=z_1+(z_2-z_1)t):}`

thus in our case:

`{(x=1-5t),(y=3),(z=2-2t):}`

We can easily see that the value `t=0` corresponds to the first point and the value `t=1` corresponds to the second.