Find the parametric equation of a line that contains (2, -1, 1) and is parallel to the vector (3, 0.5, 0).

Answer 1

To find the parametric equation of a line, we need a point on the line and a vector parallel to the line.

Given that the line is parallel to the vector (3, 0.5, 0), we can use this vector as the direction vector for our line.

Let's start with the point (2, -1, 1) and the vector (3, 0.5, 0) to find the parametric equations.

The parametric equations for a line can be written in the form:
x = x₁ + at,
y = y₁ + bt,
z = z₁ + ct,

where (x₁, y₁, z₁) is a point on the line, (a, b, c) is the direction vector, and t is a parameter.

In this case, x₁ = 2, y₁ = -1, z₁ = 1, and (a, b, c) = (3, 0.5, 0).

So, the parametric equations for the line are:
x = 2 + 3t,
y = -1 + 0.5t,
z = 1 + 0t.

Simplifying, we find:
x = 2 + 3t,
y = -1 + 0.5t,
z = 1.