AP PreCalculus Flashcards: Vectors
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 16 cards to help you master important concepts.
How do you determine a unit vector in the same direction as a given nonzero vector?
Scalar multiply the given vector by the reciprocal of its own magnitude.
Card 1 of 16
All Flashcards (16)
How do you determine a unit vector in the same direction as a given nonzero vector?
Scalar multiply the given vector by the reciprocal of its own magnitude.
How would you determine the sum of the vectors <x₁, y₁> and <x₂, y₂>?
You would create a new vector by adding the corresponding components: <x₁ + x₂, y₁ + y₂>.
What is the relationship between a vector's components and its magnitude?
The magnitude is the square root of the sum of the squares of the components, based on the Pythagorean theorem.
What is meant by the 'magnitude' of a vector?
The magnitude of a vector is the length of its corresponding line segment.
You calculate the dot product of two nonzero vectors and the result is zero. What can you determine about the angle between them?
You can determine that the vectors are perpendicular, meaning the angle between them is 90 degrees.
What is a vector?
A vector is a directed line segment. The length of the line segment is the magnitude of the vector.
How is the sum of two vectors in R^2 determined?
The sum is a new vector whose components are found by adding the corresponding components of the original vectors.
How is the magnitude of the vector <a, b> calculated?
The magnitude is found by taking the square root of the sum of the squares of the components.
What is the dot product of two vectors, <a₁, b₁> and <a₂, b₂>?
The dot product is the sum of the products of their corresponding components: a₁a₂ + b₁b₂.
If you are asked to determine the angle between two vectors, what two calculations involving the vectors must you perform first?
You must first determine the dot product of the vectors and the magnitude of each individual vector.
How can the dot product be used to determine the angle between two vectors?
The dot product is equal to the product of the vectors' magnitudes and the cosine of the angle, allowing the angle to be calculated.
What is the geometric meaning of the dot product?
The dot product is geometrically equivalent to the product of the magnitudes of the two vectors and the cosine of the angle between them.
What does a dot product of zero imply for two nonzero vectors?
If the dot product of two nonzero vectors is zero, then the vectors are perpendicular.
How would you determine the dot product of two vectors?
Multiply the first components of each vector, multiply the second components, and then add these two products together.
What is a unit vector?
A unit vector is a vector with a magnitude of 1.
What are the two primary characteristics of a vector?
A vector is characterized by its magnitude (length) and its direction.