Vectors

Definition

Vectors are quantities that have both magnitude and direction. They are used to represent physical quantities such as displacement, velocity, and electric field.

5 Must Know Facts For Your Next Test

1. Vectors can be added using the head-to-tail method or by breaking them into components and adding the components separately.
2. The magnitude of a vector can be found using the Pythagorean theorem if its components are known: $|\vec{A}| = \sqrt{A_x^2 + A_y^2}$ in two dimensions.
3. Unit vectors are dimensionless vectors with a magnitude of one, typically used to indicate direction.
4. The dot product (scalar product) of two vectors is defined as $\vec{A} \cdot \vec{B} = |\vec{A}||\vec{B}| \cos(\theta)$, where $\theta$ is the angle between the vectors.
5. In physics, vectors are crucial for describing forces, motion in two dimensions, and electric fields around multiple charges.

Review Questions

• How do you find the resultant vector when adding two vectors graphically?
• What is the difference between a scalar and a vector quantity?
• Describe how to calculate the magnitude of a vector given its components.

Related terms

Displacement:

A vector quantity representing the change in position of an object. It has both magnitude and direction.

Electric Field:

A field around charged particles that exerts force on other charged particles. Represented by electric field lines indicating direction and strength.

Component Vectors: Projections of a vector along coordinate axes. For vector $\vec{A}$ in two dimensions, these are $A_x$ and $A_y$.