Thread: 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.

Thanks for your help.

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.

Thanks for your help.

Are you told anything about vectors $\displaystyle \displaystyle \textrm{a}$ or $\displaystyle \displaystyle \textrm{b}$, or are they arbitrary?

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

$\displaystyle a\times b=i-j+k$ so the line is $\displaystyle \begin{align*}x &=1+t\\y &=3-t\\z &=t \end{align*}$

And, of course, you find the "symmetric equations" for the line by solving each of those for t and setting them equal.