Practice question · Numerical answer
Find the value of k for which the planes x + 2y + kz = 1 and 3x - y + 2z = 4 are perpendicular.
Hints
- Two planes are perpendicular when their normal vectors are orthogonal.
- Set (1, 2, k) dotted with (3, -1, 2) equal to zero.
Show the answer
-0.5 (answers within ±0.01 count)
Why
The normals dot to 3 - 2 + 2k = 1 + 2k, and setting that to zero gives k = -0.5. The whole question reduces to a dot product on the coefficient vectors, the payoff of representing planes by their normals.
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