equation of a line through a point, parallel to a plane, and perpendicular to a line

**sgcb** · August 30th 2012, 12:46 PM

Q: Find parametric equations for the line through the point (0, 1, 2) that is parallel to the plane $x+y+z=2$ and perpendicular to the line $x=1+t, y=1-t, z=2t$

I'm having trouble coming up with a sensible approach to this problem (my understanding of point/line/plane interaction is a bit shaky as solutions to similar problem have been found by applying methods used in the book examples)

I know an equation of a line is given by $\vec{r}=\vec{r_{0}}+t\vec{v}$ where $\vec{r_{0}}$ is position vector of a point on the line and $\vec{v}$ is a vector parallel with the line. The vector, $\vec{n}=[1, 1, 1]$ , is the normal vector for the parallel plane, and $\vec{v}=[1, -1, 2]$ is the vector in the direction of the perpendicular line. Is this all I need to solve? If so, where do I go from here?

**Plato** · August 30th 2012, 12:56 PM

Originally Posted by sgcb

Q: Find parametric equations for the line through the point (0, 1, 2) that is parallel to the plane $x+y+z=2$ and perpendicular to the line $x=1+t, y=1-t, z=2t$

The direction vector you need is $<1,1,1>\times<1,-1,2>$ .

Thread: equation of a line through a point, parallel to a plane, and perpendicular to a line

LinkBack

Thread Tools

Display

equation of a line through a point, parallel to a plane, and perpendicular to a line

Re: equation of a line through a point, parallel to a plane, and perpendicular to a l

Similar Math Help Forum Discussions

An equation of the line containing the given point and perpendicular to the line

Point that is perpendicular to a line of a plane?

equation of plane that contains P and perpendicular to line

vector equation of line through point perpendicular to plane

[SOLVED] Equation of a plane which parallel to a line

Search Tags