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Use direction vectors to determine if each line intersects the plane 3x-2y+4z=5. r=[-3,2,7]+t[3,6,2]

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I gotta sleep soon, so if you could help me promptly, that would be appreciated.
Sorry, I'm a little dim-witted, but isn't "0=-10" a bit, illogical? I'm being a bit confrontational because it doesn't look like my example in the txtbook, even though I don't understand it.
i was just trying to find the value of t so i let t=0 and to see how far i was off then just find t

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Where'd you get those numbers in the brackets from?
im wrong
r=(-3,2,7)+t(3,6,2) r=(-3+3t,2+6t,7+2t) sub in 3x-2y+4z=5 3(-3+3t)-2(2+6t)+4(7+2t)=5 -9+9t-4-12t+28+8t=5 15+5t=5 5t=-10 t=-2
So my goal is to solve for t?
what values of t work so yes
Cause the answer section just says yes, no, yes, yes, something. How do I know if either yes or no?
well one works so yes?
So, If I get a value for t, it must be a yes?
I'm going to cry when I forget this in the morning.
does your answer book say yes ?
Yes, it says Yes.
That makes me giggle like a little schoolgirl.
if you had the equation y=2x + 3 does the point (3,9) lie on the line yes it does .. check sub it in 9=(2)(3)+3 9=9 true now when you make 3 planes x,y,z your just check does the point lie on the plane they use word points and vector interchangeably
I'll just say yes. So If I have a value for t, it's a yes?
Ehhh, Imma sleep now. I'll be lookin at this in the morning, if I get up at the right time. Merci beaucoup!

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