Parallel lines have constant distance between them. Perpendicular lines intersect at 90-degree angles. Straight lines can be parallel, perpendicular or have one point of intersection
Vertical lines run straight up and down without inclination. All points on a vertical line have the same x-coordinate. Vertical lines are parallel to the y-axis and perpendicular to the x-axis. The slope of a vertical line is undefined
A line is formed by connecting two points with minimum distance. A segment has definite beginning and end points. A ray has only one fixed point. A line segment has fixed length
Collinear points lie on the same straight line. Collinearity is the property of points being collinear. Collinear points can exist on different planes but not different lines. Only one line can pass through three collinear points
Two geometric objects are perpendicular if their intersection forms right angles at a foot. Perpendicularity extends to lines, planes, and segments. Perpendicularity is symmetric, meaning perpendicular lines are always parallel
Quaternions were invented by William Rowan Hamilton while walking on Royal Canal. Hamilton scratched fundamental formula into Brougham bridge stone. Quaternions are noncommutative but associative, forming a group. Can be written as linear combination of real and imaginary parts