Practice question · Numerical answer
A plane has the form 2x + y - z = d and passes through the point (1, 2, 3). Find d.
Hints
- Substitute the coordinates of the point into the left-hand side.
- 2(1) + 2 - 3.
Show the answer
1
Why
2(1) + (2) - (3) = 1, so d = 1. The coefficients fix the plane's orientation via the normal (2, 1, -1), and d selects which of the parallel family actually passes through the given point.
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