Vectors are quantities that have both magnitude and direction. They are used to represent physical quantities such as displacement, velocity, and electric field.
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Vectors can be added using the head-to-tail method or by breaking them into components and adding the components separately.
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.
Unit vectors are dimensionless vectors with a magnitude of one, typically used to indicate direction.
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.
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 $A_y$.