Question

Find a vector equation and parametric equations for the line. (Use the parameter t.)The line through the point (4, 2.1, 3.1) and parallel to the vector 3i + 2j − k.

Answer 1

Answer:

Vector equation:

$(4 + 6t, 2.1 + 4t, 3.1 - 2t)$

Parametric equations:

$x(t) = 4 + 6t$

$y(t) = 2.1 + 4t$

$z(t) = 3.1 - 2t$

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:

$x(t) = 4 + 6t$

$y(t) = 2.1 + 4t$

$z(t) = 3.1 - 2t$

The vector equation is:

$(4 + 6t, 2.1 + 4t, 3.1 - 2t)$