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Vector quantities consist of both magnitude and direction. The magnitude is made up of a number and a unit. Scalar quantities consist of only a magnitude. Position, displacement, velocity, acceleration, force, weight, and momentum are examples of vector quantities. Scalar quantities include such things as mass, time, distance, speed, work, and energy, to name but a few. Vector quantities are represented on a diagram by a directed line segment, drawn to scale, with reference coordinates to show direction. The tail of a vector is called the origin and the tip is called the terminal point. Equivalent vectors have the same magnitude and direction. Collinear vectors can be added algebraically or graphically. The resultant vector is obtained from vector addition. Graphical addition of vectors is performed on a neat, accurate, scale diagram. Non-collinear vectors exist in more than one dimension. The sum of any two or more vectors can be determined graphically or mathematically. Vectors are added by aligning the tail of one vector (origin) with the tip of another vector (terminal point) on a neat, accurate, properly scaled diagram. The vector sum of two or more vectors is called the resultant vector. The resultant vector points from the tail of the first vector to the tip of the last vector being added. To make a vector negative, change its direction. A negative vector has the opposite direction of a positive vector. The magnitude and direction must be stated for the resultant vector, as for any other vector quantity. Vector and scalar operations yield very different results. The two must not be confused. To add vectors there are two techniques available, geometric addition and algebraic addition. Both yield the same result. The choice of which technique to use in adding vectors depends on the application and is a matter of convenience. Since a vector is defined by its magnitude and direction, changing its location in our reference frame without changing its direction or magnitude leaves it the same vector. We are free to relocate a vector anywhere in our space where we find it convenient. To add vectors geometrically you just place the tail of one at the head of the other.
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