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The question is in the paint doc.
My solution:
I created a matrix
1. first row: 1,1,12 which represents the equation of the plane x + y  z = 2
second row: 2,1,31 .... 2x  y + 3z = 1
2. I came up with the parametric equation:
x = 1 2/3t
y = 1 + 5/3t
z=t
3. The vector that represents this line is:
<2/3,5/3,0> = <2,5,0>
4. A point on the line is (1,1,0)
5. <1,2,1>  <1,1,0> = <2,1,1> ... Vector // to plane Note: (1,2,1) is a point on the plane.
6. <2,1,1> x <2,5,0> = <5,2,8>
7. 5(x1) + 2(y1) + z = 0
or
5x + 2y + z = 7
The answer in the back of the book is: x  2y + 4z = 1
My solution:
I created a matrix
1. first row: 1,1,12 which represents the equation of the plane x + y  z = 2
second row: 2,1,31 .... 2x  y + 3z = 1
2. I came up with the parametric equation:
x = 1 2/3t
y = 1 + 5/3t
z=t
3. The vector that represents this line is:
<2/3,5/3,0> = <2,5,0>
4. A point on the line is (1,1,0)
5. <1,2,1>  <1,1,0> = <2,1,1> ... Vector // to plane Note: (1,2,1) is a point on the plane.
6. <2,1,1> x <2,5,0> = <5,2,8>
7. 5(x1) + 2(y1) + z = 0
or
5x + 2y + z = 7
The answer in the back of the book is: x  2y + 4z = 1
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