How do you find parametric equations for the line through P-naught=(3,-1,1) perpendicular to the plane 3x+5y-7z=29?

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Answer 1 · 2016-06-10T17:09:38

# { (x = 3 + lambda 3), (y = -1+lambda 5), (z = 1 -lambda 7) :}#

Plane #Pi->3x+5y-7z=29# can be written as

#<< vec v , p-p_0 >> = 0#

in which #p = {x,y,z}, p_0 = {x_0,y_0,y_0} # and #vec v# is a normal vector to the plane and #p-p_0# are segments pertaining to the plane.

For #Pi# we have #vec v = {3,5,-7}# so the line perpendicular to #Pi# passing by #q_0 = {3,-1,1}# is

#l->p = q_0 + lambda vec v# or

# { (x = 3 + lambda 3), (y = -1+lambda 5), (z = 1 -lambda 7) :}#