# Finding parametric equations through a point and perpendicular to vectors

• Sep 7th 2011, 12:31 AM
florx
Finding parametric equations through a point and perpendicular to vectors
Find parametric equations and symmetric equations for the line through a point Po(1,3,0) and perpendicular to vectors a and b.

a = i + j
b = j + k

I need help finding out the parametric equations for this. In order to solve it would we need to cross a and b and then do the formula a + tv?

where v is equal to axb.

• Sep 7th 2011, 01:01 AM
Prove It
Re: Finding parametric equations through a point and perpendicular to vectors
Quote:

Originally Posted by florx
Find parametric equations and symmetric equations for the line through a point Po(1,3,0) and perpendicular to vectors a and b.

a = i + j
b = j + k

I need help finding out the parametric equations for this. In order to solve it would we need to cross a and b and then do the formula a + tv?

where v is equal to axb.

Are you told anything about vectors $\displaystyle \textrm{a}$ or $\displaystyle \textrm{b}$, or are they arbitrary?
• Sep 9th 2011, 01:23 PM
Plato
Re: Finding parametric equations through a point and perpendicular to vectors
Quote:

Originally Posted by florx
Find parametric equations and symmetric equations for the line through a point Po(1,3,0) and perpendicular to vectors a and b.
a = i + j
b = j + k

$a\times b=i-j+k$ so the line is \begin{align*}x &=1+t\\y &=3-t\\z &=t \end{align*}
• Sep 10th 2011, 03:34 AM
HallsofIvy
Re: Finding parametric equations through a point and perpendicular to vectors
And, of course, you find the "symmetric equations" for the line by solving each of those for t and setting them equal.