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Stitz-Zeager_College_Algebra_e-book

# Scalar multiplication 864 component form 859

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Unformatted text preview: v . Since we can reconstruct − − → v completely from P and Q, we write v = P Q, where the order of points P (initial point) and Q (terminal point) is important. (Think about this before moving on.) Q (4, 6) P (1, 2) − − → v = PQ While it is true that P and Q completely determine v , it is important to note that since vectors are deﬁned in terms of their two characteristics, magnitude and direction, any directed line segment with the same length and direction as v is considered to be the same vector as v , regardless of its initial point. In the case of our vector v above, any vector which moves three units to the right and four up3 from its initial point to arrive at its terminal point is considered the same vector as v . The notation we use to capture this idea is the component form of...
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