NY Regents Geometry Vectors — practice questions

1. A vector is drawn as a directed line segment with an arrowhead. 2. The length of that segment is its magnitude. 3. The way the arrowhead points is its direction. 4. The starting point is not part of the identity, which is why a vector can be slid to the origin. _Source: OpenStax Precalculus (CC BY 4.0), Ch 8 "Further Applications of Trigonometry", section 8.8 Vectors_

1. The magnitude is found by the Pythagorean Theorem on the two components. 2. Squaring gives 81 and 144, which add to 225. 3. The square root of 225 is 15. 4. So the magnitude is 15 units. 5. Answering 21 units adds the components instead of squaring, adding, then taking the root. _Source: OpenStax Precalculus (CC BY 4.0), Ch 8 "Further Applications of Trigonometry", section 8.8 Vectors_

1. A vector carries only two pieces of information, its magnitude and its direction. 2. Two vectors match exactly when both pieces agree. 3. Where each one starts is irrelevant, since both reduce to the same position vector. 4. Opposite directions cannot give equality, however well the lengths match. _Source: OpenStax Precalculus (CC BY 4.0), Ch 8 "Further Applications of Trigonometry", section 8.8 Vectors_