Flashcards on A vector and its coordinates
Understanding a Vector and Its Coordinates: A Student Guide
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Introduction to Vectors
14 cards
Card 1
Question: What is the difference between a scalar and a vector quantity?
Answer: A scalar quantity is defined solely by its magnitude, while a vector quantity possesses both magnitude and direction.
Card 2
Question: Give three examples of scalar quantities.
Answer: Temperature, mass, and time.
Card 3
Question: Give three examples of vector quantities.
Answer: Displacement, velocity, and force.
Card 4
Question: How is a vector visually represented?
Answer: A vector can be visually represented by an oriented line segment (directed line segment) with a starting point, an ending point, and an arrowhead indi
Card 5
Question: If points A and B define a vector, how is it typically denoted?
Answer: It is often denoted as **AB** or simply **a**.
Card 6
Question: What does it mean for vectors to be 'free vectors'?
Answer: Any two oriented line segments that have the same length and point in the same direction represent the same vector, and these are called free vectors.
Card 7
Question: What are position vectors?
Answer: Position vectors are vectors placed with their initial point at the origin (0, 0, 0) of a coordinate system, defining the position of their terminal p
Card 8
Question: How is a 2D vector originating from the origin represented by coordinates?
Answer: A vector **v** originating from the origin (0, 0) and terminating at P(vₓ, vᵧ) is represented by its coordinates (vₓ, vᵧ).
Card 9
Question: How is a 3D vector originating from the origin represented by coordinates?
Answer: A vector **v** originating from the origin (0, 0, 0) and terminating at P(vₓ, vᵧ, v_z) is represented by its coordinates (vₓ, vᵧ, v_z).
Card 10
Question: How do you find the coordinates of a vector **PQ** connecting two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂)?
Answer: The coordinates are found by subtracting the coordinates of the initial point from the coordinates of the terminal point: **PQ** = (x₂ - x₁, y₂ - y₁,