hellawowser
New member
- Joined
- Sep 25, 2017
- Messages
- 23
Line perpendicular to two skew lines
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 commom points.
s: x = 1-2b , y =2+b , z= b
Also, the normal vector of their planes 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 .
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 commom points.
s: x = 1-2b , y =2+b , z= b
Also, the normal vector of their planes 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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