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Determine the value for "x" such that the points A(-1, 3, 3), B(-2, 3, -1), and C(-5,6, "x") all lie on a plane that contains the origin.?
Here's what I've done (doesn't give me the right answer):
Eq 1. -1m-2n = -5
Changes to: m=-5+2n
Eq 2. 3m+3n=6
Eq 3. 4m-n="x"
Substitution (Eq 2 and 1):
3(-5+2n)+3n=6
-15+9n=6
9n=21
n=21/9
When I replace "n" with 21/9 in Eq. 3, I don't get the same number meaning the vectors don't even lie on the plane (which goes against what the questions says).
Help please!
1 Answer
- ?Lv 77 years agoFavorite Answer
If A, B, C and O are all in the one plane then C = aA+bB
(-5,6,x) = a(-1, 3, 3)+b(-2, 3, -1)
-a-2b=-5, 3a+3b=6 and 3a-b=x
Simultaneously solve the first two equations to get a=-1 and b=3
Substitute them into the third equation to get x = -6
