(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]

2. Relevant 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]

3. 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]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Simple Vector Problem

**Physics Forums | Science Articles, Homework Help, Discussion**