Question

Which of these three points falls on the line?

l: r(t)=(i+2j)+t(6i+j-5k)

P(1,2,0); Q(-5,1,5); R(-4,2,5)

P:
(1+6t) = 1
t=0

2=2+t
t=0

t=0

Q:
-5=1+6t
t=-1

1=2+t
t=-1

t=0

R:
-4=1+6t
t=-5/6

2=t+2
t=0

t=0

I have the answer, but I don't understand why P and Q fall on the line but R does not. Is it because the i and j magnitudes are different for R?

Answer 1

I see you updated the question, so where are you stuck? You solve one individual line for \(t\) and then plug it into the remaining lines and check if it doesn't give you any contradictions, if it doesn't then the point is on the line, if it does give you a contradiction, the point is not on the line.