Answer:
Vector equation:
[tex](4 + 6t, 2.1 + 4t, 3.1 - 2t)[/tex]
Parametric equations:
[tex]x(t) = 4 + 6t[/tex]
[tex]y(t) = 2.1 + 4t[/tex]
[tex]z(t) = 3.1 - 2t[/tex]
Step-by-step explanation:
The line is parallel to the vector 3i + 2j − k.
So the vector of this line is a multiple of this vector, so i will use 6i + 4j - 2k.
The line goes through the point (4, 2.1, 3.1).
So the parametric equations are:
[tex]x(t) = 4 + 6t[/tex]
[tex]y(t) = 2.1 + 4t[/tex]
[tex]z(t) = 3.1 - 2t[/tex]
The vector equation is:
[tex](4 + 6t, 2.1 + 4t, 3.1 - 2t)[/tex]
