How could you find a set of parametric equations for the line thru the points (3, 2, 4) & (2, 1, 3)?

Question

possible sets of parametric equations to choose from....

a. x = 2 + t, y = 1 + 3t, z = 3 - 2t
b. x = 2 + t, y = 1 + 4t, z = 3 - 2t
c. x = 2 + 2t, y = 1 + 3t, z = 3 - 2t
d. x = 2 + t, y = 1 + 4t, z = 3 - t
e. x = 2 + t, y = 1 + t, z = 3 + t
f. x = 2 + 2t, y = 1 + 4t, z = 3 + 3t
g. none of these

Answer 1

line in n-space is point plus multiple of direction vector. so L = (3,2,4) + t(-1,-1,-1) or L = (2,1,3) + t(1,1,1). That's e.

Answer 2

f. x = 2 + 2t, y = a million + 4t, z = 3 + 3t direction vector = (4 5 6) - (2 a million 3) = (2 4 3) place vector would be the two (4 5 6) or (2 a million 3). Equation: l: r = (2 a million 3) + t(2 4 3)