The line of intersection of the planes x + y = 0 and z = 3 is, in parametric form: r = ⟨0, 0, 3⟩ + λ⟨1/√2, -1/√2, 0⟩. To find this result:
Normalize the normal vectors:
n1 = ⟨1/√2, 1/√2, 0⟩ and n2 = ⟨0, 0, 1⟩.
Find the coefficients for the parametric equation: k1 = 0 and k2 = 3.
Compute the cross product of the vectors: n1 × n2 = ⟨1/√2, -1/√2, 0⟩.
Compute the following:
r = (k1n1 + k2n2) + λ(n1 × n2) = ⟨0, 0, 3⟩ + λ⟨1/√2, -1/√2, 0⟩.
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