Question

Suppose the solution set of a certain system of linear equations can be described as ________, ________, with ________. Use vectors to describe this set as a line in 3D.

Answer 1

To describe a solution set of a system of linear equations as a line in 3D using vectors, we need to determine the direction of the line and a point on the line. The equation of the line can be written as r = p + tv, where r represents any point on the line, t is a scalar parameter, and v is the direction vector.

Step-by-step explanation:

To describe a solution set of a system of linear equations as a line in 3D using vectors, we need to determine the direction of the line and a point on the line. Let's assume the direction vector is v and the point vector is p. The equation of the line can be written as r = p + tv, where r represents any point on the line, t is a scalar parameter, and v is the direction vector.

For example, if the solution set is described as (2, 3, 4), (5, 6, 7), with a direction vector of (1, 1, 1), we can choose (2, 3, 4) as the point vector p and (1, 1, 1) as the direction vector v. The equation of the line would then be r = (2, 3, 4) + t(1, 1, 1).