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JoshHolloway
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Homework Statement
Find a plane that is perpendicular to the line [tex] \vec{L}(t) = (5,0,2)t + (3,-1,1)[/tex] and passes through the point [tex] (5,-5,0) [/tex]
Homework Equations
The equation of the plane that P through [tex] (x_{0},y_{0},z_{0}) [/tex] that has a normal vector [tex] \vec{n} = A \vec{i} + B \vec{j} + C\vec{k} [/tex] is:
[tex] A(x - x_{0}) + B(y - y_{0}) + C(z - z_{0}) = 0 [/tex]
that is, [tex] (x,y,z) \in P [/tex]
The Attempt at a Solution
[tex] \vec{L}(t) = (5t + 3, -1, 2t + 1) [/tex]
let [tex] t = 1 \Rightarrow \vec{L}(1) = (8,-1,3) = (A,B,C)[/tex]
[tex](x_{0},y_{0},z_{0}) = (5,-1,0) [/tex]
[tex] A(x - x_{0}) + B(y - y_{0}) + C(z - z_{0}) = 0 [/tex]
[tex](8)(x - 5) + (-1)(y +1) + (3)(z - 0) = 0 [/tex]
[tex]8x - 40 - y -1 + 3z = 0; [/tex]
[tex]8x - y + 3z = 41 [/tex]
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