Help with calculus! vector parametrization...?

Question

Find the vector parametrization for the line that passes through (1,1,1) parallel to the line through (2,0,-1) and (4,1,3). Please show all your work.

Answer 1

Greetings,

the line through (2,0,-1) and (4,1,3) has the vector (2,1,4)

the line through (1,1,1) and parallel to (2,1,4)

(1,1,1) + t(2,1,4) = (1 + 2t, 1 + t, 1 + 4t), where t is a real number

Regards