What makes two vectors equal

We will be comparing two vectors, a and b. They could be forces, or velocities, or accelerations; it doesn't really matter. Example 1: We have two vectors with the same direction, but the magnitudes or length of the vectors are different. Vector a does not equal vector b in this example. This example seems pretty simple, because the same rule applies for scalars; if the magnitude is different, the quantities are not equal.

An object weighing 50 pounds is not equal to an object weighing 25 pounds. Example 2: This example is a little more complex. In this case, we have two vectors with equal magnitude, but the directions are different. If the vector was a velocity, this tells us that a car traveling 45 mph to the northeast will end up in a different place than another car also traveling 45 mph due east.

In one hour, they will both move 45 miles, but the locations will be different. In two hours, they will be even farther apart. Example 3: In this example, we have two vectors with equal length and equal direction.

Vector is equal to vector b. Equal vectors may start at different positions. Note that when the vectors are equal, the directed line segments are parallel. Equality Of Column Vectors If two vectors are equal then their vector columns are equal. Example: The column vectors p and q are defined by. When are two vectors equal? Two vectors are equal if they have the same length magnitude and direction.

What are the conditions necessary for vectors to be considered equal? Two vectors are equal if they have the same length and direction and are parallel. What is a negative vector? Example: Are vectors u and w equivalent?