# Linear Algebra

Help me find my error!
a)Write down the equation of the plane passing through the point (1,5,7) and parallel to the lines.

Line A: Line B: Point
x = 3- 2t x = 2 - 2t <1,5,7>
y = 1 - 5t y = 3 - 2t
z = 2 - t z = 1 + 4t

Parametric equation of the plane
<x,y,z> = <1,5,7> + t1 <-2,-5,-1> + t2 <-2,-2,4>

Equation of the plane
<-2,-5,-1> x <-2,-2,4> = -18i - 6j - 6k

-18(x-1) -6 (y-5) -6 (z-7)
-18x +18 -6y + 30 - 6z + 42

-18x - 6y - 6z + 90 = 0 <---My answer
-11x + 5y - 3z +7 = 0 <--- The textbook solution

Where have I gone wrong?

1. 👍 0
2. 👎 0
3. 👁 187

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