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.
40 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a vector?
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A quantity having both magnitude and direction- What is the magnitude of a vector?
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Its length, calculated similarly to distance- What is a vector's direction typically described by?
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An angle relative to a reference axis- What is vector addition, geometrically?
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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?
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Drawing vectors from the same point and forming a parallelogram, with the diagonal as the sum- What is scalar multiplication of a vector?
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Multiplying a vector's magnitude by a number, keeping or reversing its direction- What is a unit vector?
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A vector with a magnitude of exactly 1- What are component form vectors?
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Vectors expressed as ordered pairs or triples showing horizontal and vertical (and depth) parts- What is the dot product of two vectors?
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A scalar value found by multiplying corresponding components and summing them- What does a dot product of zero indicate about two vectors?
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They are perpendicular (orthogonal)- What is the formula for a vector's magnitude given its components (a, b)?
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sqrt(a^2 + b^2)- What are the standard unit vectors in two dimensions?
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i (1,0) and j (0,1)- What is a resultant vector?
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The vector sum of two or more vectors- What real-world quantity is commonly represented by vectors, involving both speed and heading?
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Velocity- What real-world quantity, involving both size and direction, is also represented by vectors?
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Force
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