Finding a plane given a line and plane ortogonal

1. Homework Statement

Find a plane containing the line r(t) = <5,5,-1> + t<-6,-7,-7> and orthogonal to the plane -5 x + 5 y -2 z = 1

3. The Attempt at a Solution

I...honestly have no idea where to even begin. I don't recall ever being taught how to find a plane given a line and the orthogonal plane. I know how to do it with three points and 1 point plus a line and two vectors...but not a line and an orthogonal plane...could someone point me in the right direction?

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Here goes my best guess ( i'm sorry am new at this forum )

get the orthogonal plane and use it to express a vector ( -5i , 5j , -2k ) call it 'a'
then using the scalar product rule express the other vector r(t) = 'b' but make the line within 'b' hit a point in the plane. that is easy .. you may already know

since the formula is

cos thetha = (a·b) / |a||b|

if thetha = 0 then both planes will be orthogonal .. however this is my best fast guess, i know there will be someone who can help you better .. my response just quite sucks .. sorry

HallsofIvy