I've been given these two lines and need to find the

equation of a l line that is perpendicular to BOTH . What i've done so far:

r : x = 2+3a , y = 2 , z= 3-2a Checked and they aren't

parallel and don't have any common points.

s: x = 1-2b , y =2+b , z= b

Also, the normal vector of their plans is (2,1,3) . The plan of r is 2(x-2) +1(y-2) + 3(z-3) = 0 and the plan of s is 2(x-1) + 1(y-2) + 3(z) = 0.

Thinking of a vector that is parallel to l , it is (l1,l2,l3) and its dot product with the vectors parallel to the other 2 lines equals 0

(l1,l2,l3) * (3,0,-2) =0

(l1,l2,l3) * (-2,1,1) = 0

3l1 - 2l3 = 0

-2l1 + l2 + l3 = 0

Here's where i'm stuck .

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