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In this lesson, we will learn how to determine if the given vectors are parallel.

Related Topics: More Lessons on Vectors

A vector is a quantity that has both magnitude and direction.

Vectors are parallel if they have the same direction. Both components of one vector must be in the same ratio to the corresponding components of the parallel vector.

* Example: *

Two vectors are parallel if they are scalar multiples of one another.

If

The following diagram shows several vectors that are parallel.

Example: Determine which vectors are parallel to

Lines are parallel if the direction vectors are in the same ratio.

Example: If the lines l

Examples:

(1) A, B, C are midpoints of their respective lines. Find the vector OB.

(2) N = midpoint of OB, M = midpoint of OA. Show that MN is parallel to AB.

(3) Given the vectors, prove that the three given points are collinear.

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.