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# Parallel Planes Question Watch

1. Let the Line L1 be defined as -

x = 1+t
y = 2-t
z = 1+2t

Let the Line L2 be defined as -

x = 3+t
y = 4-t
z = 1-2t

Find the equations of two parallel planes A and B such that
L1 ⊆ A and L2 ⊆ B

2. 1. Do you see how a point on L1 is (1,2,1) and a point on L2 is (3,4,1)?
2. Do you see that if a plane is parallel to two lines, then it has to be able to extend towards BOTH lines' directional vectors?
3. Do you know that the vector equation of a plane is a+d1+d2 (position + direction1 + direction2)?
3. (Original post by aznkid66)
1. Do you see how a point on L1 is (1,2,1) and a point on L2 is (3,4,1)?
2. Do you see that if a plane is parallel to two lines, then it has to be able to extend towards BOTH lines' directional vectors?
3. Do you know that the vector equation of a plane is a+d1+d2 (position + direction1 + direction2)?
Taking the cross product would give me a normal to the required plane I suppose.

After that, I plug in the points (1,2,1) and (3,4,1) to get two different constants c in the plane equation x+y+z= c

4. Yup, that would also work. I'm guessing you need to find the equation of the plane in cartesian form? I was suggesting a different form in my post ^^;

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Updated: April 11, 2013
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