Precalculus, Unit 6: Vectors and Parametric Equations. Key terms, formulas, and worked-example cues a high school student meets for this unit, building on prior units. Front: the term, formula name, or short problem cue. Back: the definition, formula, or solution method.
30 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a vector?
- A quantity having both magnitude and direction
- What is the magnitude of a vector?
- Its length, calculated similarly to distance
- What is a vector's direction typically described by?
- An angle relative to a reference axis
- What is vector addition, geometrically?
- Placing vectors head to tail and drawing a vector from the first's tail to the last's head
- What is the parallelogram rule for adding vectors?
- Drawing vectors from the same point and forming a parallelogram, with the diagonal as the sum
- What is scalar multiplication of a vector?
- Multiplying a vector's magnitude by a number, keeping or reversing its direction
- What is a unit vector?
- A vector with a magnitude of exactly 1
- What are component form vectors?
- Vectors expressed as ordered pairs or triples showing horizontal and vertical (and depth) parts
- What is the dot product of two vectors?
- A scalar value found by multiplying corresponding components and summing them
- What does a dot product of zero indicate about two vectors?
- They are perpendicular (orthogonal)
- What is the formula for a vector's magnitude given its components (a, b)?
- sqrt(a^2 + b^2)
- What are the standard unit vectors in two dimensions?
- i (1,0) and j (0,1)
- What is a resultant vector?
- The vector sum of two or more vectors
- What real-world quantity is commonly represented by vectors, involving both speed and heading?
- Velocity
- What real-world quantity, involving both size and direction, is also represented by vectors?
- Force
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