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Find parametric equations of a line that intersects both l1 and l2 at right angles:

l1= [x,y,z]=[4,8,-1] + t[2,3,-4]

l2= x-7/-6 = y-2/1 = z+1/2

I found the cross product of l1 and l2 to get a normal vector perpendicular to both, which is [10, 20, 20] or n=[1,2,1]

Now I am not sure how to get the parametric equation for the line because I cannot just use one of the vectors from above, like [4,8,-1] because it is not necessarily on l3.

l1= [x,y,z]=[4,8,-1] + t[2,3,-4]

l2= x-7/-6 = y-2/1 = z+1/2

I found the cross product of l1 and l2 to get a normal vector perpendicular to both, which is [10, 20, 20] or n=[1,2,1]

Now I am not sure how to get the parametric equation for the line because I cannot just use one of the vectors from above, like [4,8,-1] because it is not necessarily on l3.

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