Solution: The parallel line through the point has the vector equation L = < 0, 1, 2 > + t < a, b, c >, and we have to determine a, b, and c.

( 1 ) L is parallel to the plane x + y + z = 2

L is perpendicular to **n** = < 1, 1, 1 >, the normal to the plane.

L and **n** are perpendicular

Thus a + b + c = 0.

( 2 ) L and the line < 1, 1, 0 > + t < 1, -1, 2 > are perpendicular

Thus a - b + 2c = 0

We have two equations with three variables:

a - b = -2c

Solving for *a* and *b* in terms of c :

2b = c b = c/2

Thus the vector equation of the line is : L = < 0, 1, 2 > + t < 3, -1, -2 > and the parametric equations are:

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by: nl
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