# Equations of perpendicular vectors passing through a specific point.

• Mar 28th 2011, 04:02 AM
darksoulzero
Equations of perpendicular vectors passing through a specific point.
Write the equations of two lines that intersect at the point A(3,1-1) and are perpendicular.

Not enough information was provided so I just used point A as the point on both of my lines : [x,y,z]= [3,1,-1]+t[1,-3,4] and [x,y,z]=[3,1,-1]+[3,1,0]. For the direction vectors I arbitrarily chose points that would yield 0 when I applied the dot product.

I'm not sure if this is correct.
• Mar 28th 2011, 04:07 AM
Plato
Quote:

Originally Posted by darksoulzero
Write the equations of two lines that intersect at the point A(3,1-1) and are perpendicular.
Not enough information was provided so I just used point A as the point on both of my lines : [x,y,z]= [3,1,-1]+t[1,-3,4] and [x,y,z]=[3,1,-1]+[3,1,0]. For the direction vectors I arbitrarily chose points that would yield 0 when I applied the dot product.

The are infinitely many correct answers to this question.
Yours is one of them.
• Mar 28th 2011, 04:49 AM
HallsofIvy
Quote:

Originally Posted by darksoulzero
Write the equations of two lines that intersect at the point A(3,1-1) and are perpendicular.

Not enough information was provided so I just used point A as the point on both of my lines : [x,y,z]= [3,1,-1]+t[1,-3,4] and [x,y,z]=[3,1,-1]+[3,1,0].

You forgot the parameter in this equation.

Quote:

For the direction vectors I arbitrarily chose points that would yield 0 when I applied the dot product.

I'm not sure if this is correct.
(It would be better to say you arbitrarily chose vectors that had dot product 0.)

Other possible answers would be, say [3, 1, -1]+ t[1, 0, 0] and [3, 1, -1]+ t[0, 1, 0]. [3, 1, 1]+ t[0, 0, 1] would be a [b]third[b] line perpendicular to both of those.