Question

What are the parametric equations of the line through the point (-2,1,-7) and parallel to the vector?

Answer 1

The parametric equations of a line passing through (-2,1,-7) parallel to a direction vector (a, b, c) are x(t) = -2 + at, y(t) = 1 + bt, and z(t) = -7 + ct.

Step-by-step explanation:

The parametric equations of a line are used to describe a line in three-dimensional space. To write these equations, you need a point the line passes through and a direction vector that is parallel to the line. Given a point (-2,1,-7) and assuming we have a direction vector (a, b, c), the parametric equations can be written as:

• x(t) = -2 + at
• y(t) = 1 + bt
• z(t) = -7 + ct

Here, t is the parameter, which can take any real number value, and a, b, and c are the scalar components of the given direction vector.