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.
You forgot the parameter in this equation.
(It would be better to say you arbitrarily chose vectors that had dot product 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.
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.