Equal vectors

Definition

Equal vectors have the same magnitude and direction, regardless of their initial points. They can be positioned anywhere in space as long as these two properties match.

5 Must Know Facts For Your Next Test

1. Equal vectors do not need to have the same initial point.
2. The magnitudes of equal vectors are identical.
3. The directions of equal vectors are the same.
4. If two vectors are equal, their corresponding components are equal: $\vec{A} = \vec{B}$ implies $A_x = B_x$, $A_y = B_y$, and $A_z = B_z$ in three dimensions.
5. Graphically, if you translate one vector to start at the origin, it will overlap exactly with its equal counterpart.

Review Questions

• What conditions must be met for two vectors to be considered equal?
• Can two vectors with different initial points still be equal? Explain why or why not.
• If $\vec{A} = \langle 3, -4 \rangle$ and another vector is given by $\langle 3, -4 \rangle$, are they equal? Justify your answer.

Related terms

Vector Magnitude: The length or size of a vector, often denoted as $|\vec{A}|$.

Vector Direction: The orientation of a vector in space, usually specified by an angle or by its components.

Component Form: Representation of a vector using its horizontal (x) and vertical (y) components: $\vec{A} = \langle A_x, A_y \rangle$.