IBMediumVectors10–12
Where a 3D Line Crosses the xy-Plane
Onde uma Reta em 3D Atravessa o Plano xy
A line has vector equation \vec{r} = \begin{pmatrix} 1 \\ 2 \\ -1 \end{pmatrix} + t\begin{pmatrix} 2 \\ -1 \\ 3 \end{pmatrix}. Show that the point P(7, -1, 8) lies on the line, and find the point where the line crosses the plane z = 0.
A point is on the line only if one single value of the parameter reproduces all three coordinates — find a candidate from one coordinate and then test the others. For the crossing, the plane fixes one coordinate, which fixes the parameter.
Solution
Step 1 of 9
- 1.From the first coordinate: