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Find the distance of the point (1, -2, 3) from the plane x - y + z = 5 when the measurement is taken along a line parallel to x/2 = y/3 = (z-1)/6.

1. 1
2. 2
3. 4
4. 2√3

Correct answer: 1

Solution

Take the line through (1,-2,3) parallel to (2,3,-6): (1+2t, -2+3t, 3-6t). Substituting into x-y+z=5 gives 6-7t... solving 7-? gives t=1/7, and the distance is |t|*|(2,3,-6)| = (1/7)*7 = 1.

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