is the point (....) on the line (....)+t(....)?

Question

(a) Is the point (11 14 17 18) on the line (1 2 3 4) + t (5 6 7 8)?
*they are all vertically arrange like this:
(11)
(14)
(17)
(18)

(b) Does the point (4 3 2 ) lie in the plane (1 2 3) + t(1 1 0) + s(0 1 1) ?
*they are also all vertically arrange like this:
(4)
(3)
(2)
Explain your answers.

sorry for the misinterpretation,

(a) is the point (11,14,17,18) on the line (1,2,3,4) + t(5,6,7,8)?

(b) does the point (4,3,2) lie in the plane (1,2,3)+t(1,1,0)+s(0,1,1)?

Answer 1

(a) is the point (11,14,17,18) on the line (1,2,3,4) + t(5,6,7,8)?

x= 1 + 5t = 11
y = 2 + 6t = 14
z= 3+ 7t = 17
w = 4+ 8t = 18
form 1st eq. t = 2, but if you substitute 2 into the 4th eq. you see that 4 + 8(2) =20 which is not = 18
therefore the point is not on the line


(b) does the point (4,3,2) lie in the plane (1,2,3)+t(1,1,0)+s(0,1,1)?

x= 1 + 2t =4
y = 2 + t + s = 3
z = 3 + s = 2
so from 3rd eq. s = -2
then 2 + t -1 =3
1 + t = 3
so t =2
then x = 1 + 2(2) = 5 not 4, so the point is not on the plane

Answer 2

Sorry, but your terminology does not make sense.