Plane

To determine which line is parallel to the plane given by the equation , we must identify the direction vector normal to the plane and compare it with the direction vectors of the given lines.

The general form of a plane is , where is the normal vector. Therefore, the normal vector to the plane is .

For a line given in the form , the direction vector is .

We need to find a line that has a direction vector orthogonal to the normal vector . Two vectors and are orthogonal if their dot product is zero: .

Evaluating each option:

• has direction vector . Calculate . They are orthogonal, so the line is parallel.
• has direction vector . Calculate . They are not orthogonal.
• has direction vector . Calculate . They are not orthogonal.
• has direction vector . Calculate . They are not orthogonal.

The correct line parallel to the plane is .