Find the plane equation passing through the line L and parallel to the line L2. L: 2x + y-z-1 = 0 3x-2y + 2Z-2 = 0 Find the plane equation passing through the line L and parallel to L2. L: 2x + y-z-1 = 0 3x-2y + 2Z-2 = 0 L2: x = 1 y = - 2 | Math enthusiast | Mathematical art

Find the plane equation passing through the line L and parallel to the line L2. L: 2x + y-z-1 = 0 3x-2y + 2Z-2 = 0 Find the plane equation passing through the line L and parallel to L2. L: 2x + y-z-1 = 0 3x-2y + 2Z-2 = 0 L2: x = 1 y = - 2

The direction vector of L2 is s = (1,0,0) × (0,1,0) = (0,0,1)
Let the plane equation (using the plane beam) passing through the line L and parallel to L2 be
k·（2x+y－z－1）+3x－2y+2z－2=0
The normal vector of the plane
n=（2k+3,k-2,-k+2）
The plane is parallel to L2
∴ n·s=-k+2=0
The solution is k = 2
The obtained plane is: 7x-4 = 0

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