The shortest distance from (
to the line of intersection of the pair of planes
is
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First, let's manipulate the equation to make it more manageable.
x y + y z + z x + y 2 = 0
( x + y ) ( z + y ) = 0
So, 1 plane would be when x = − y and the other plane would be when z = − y
The line of intersection would be when both conditions are satisfied, as in x = z = − y
This simplifies the whole question:
L can then be easily calculated to be 3 2 2