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.

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) (Show Source): You can put this solution on YOUR website!
.


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.

RELATED QUESTIONS
'Lines in 3-Space' lesson: 1. State where possible vector, parametric, and symmetric... (answered by ikleyn)

Write a vector equation of the line that passes through point p and is parallel to line... (answered by nyc_function)

I need help. #1 find the parametric equations for line passing through the points... (answered by Alan3354)

Find the coordinates of the point where the line with parametric equations: x=1-t,... (answered by Edwin McCravy)

Find parametric equations through point P= (2,2,7) in the direction of the vector v =... (answered by ikleyn)

) Consider the line L in R^3 , given by x = −λ + 2, y = 2λ − 1,... (answered by ikleyn)

Consider the line L in R^3 , given by x = −λ + 2, y = 2λ − 1, and... (answered by ikleyn)

find the equation of a line passing through (2,-1,3) and is orthogonal to 3x-7y+5z+55=0,... (answered by robertb)

1. Find a set of parametric equations for the line which passes through the points (-2, (answered by Fombitz)