Vector equations of lines

Vector equations of lines: linear algebra practice

Write and interpret vector equations of lines in two and three dimensions. Questions connect a fixed point with a direction vector, recover a line through two points, check whether a target lies on it and compare equivalent descriptions. Real parameters are used unless a problem explicitly restricts the range.

What you will practise

• Construct a line from a point and a nonzero direction
• Evaluate and test membership in a parametric line
• Recognize equivalent parameterizations and degenerate directions

How to use this questionset

Prerequisites: Vector subtraction, scalar multiplication, span and simple coordinate equations. The questions progress from direct interpretation to application and reasoning. Work out an answer before comparing the choices; for multi-select questions, evaluate every statement independently. Worked explanations show the reasoning and address relevant misconceptions, so an incorrect attempt can guide your next review.

A nonzero direction is essential. The starting point in a formula is an anchor on the line, not necessarily an endpoint of the entire line. Line parameterizations will be converted to normal descriptions and used in shortest-distance calculations. This microlearning belongs to Module 1, Vectors and Geometry, in the Complete Linear Algebra Course.