SOLUTION: Find the vector and parametric equations for the line through the P(4,-1,-3) and orthogonal to the plane 4x+3y-3z=1.

Algebra ->  Vectors -> SOLUTION: Find the vector and parametric equations for the line through the P(4,-1,-3) and orthogonal to the plane 4x+3y-3z=1.      Log On


   

Question 1170574: Find the vector and parametric equations for the line through the P(4,-1,-3) and orthogonal to the plane 4x+3y-3z=1.
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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The vector ORTHOGONAL to the plane 4x + 3y - 3z = 1  is the vector  U = (4,3,-3).


The vector equation the problem asks for is  V(t) = P + U*t,  where  P is the given point  (4,-1,-3) and "t" is the parameter.


The parametric equation consists of the THREE SCALAR equations

    x(t) =  4 + 4t,

    y(t) = -1 + 3t,

    z(t) = -3 - 3t.

Solved, answered and explained.