 Ch 2. Vectors Multimedia Engineering Statics Scalars & Vectors 2-DVectors 3-DVectors DotProducts
 Chapter 1. Basics 2. Vectors 3. Forces 4. Moments 5. Rigid Bodies 6. Structures 7. Centroids/Inertia 8. Internal Loads 9. Friction 10. Work & Energy Appendix Basic Math Units Sections Search eBooks Dynamics Statics Mechanics Fluids Thermodynamics Math Author(s): Kurt Gramoll ©Kurt Gramoll STATICS - THEORY Vector Multiplication In the previous two sections, addition and subtraction of 2-D and 3-D vectors were illustrated. When "multiplying" two vectors, a special types of multiplication must be used, called the "Dot Product" and the "Cross Product". This section deals with only the dot product. The cross product is presented in a later section. Dot Product Dot Product Angle The dot product of two vectors A and B is defined as the product of the magnitudes A and B and the cosine of the angle θ between them:      A • B = |A| |B| cosθ The dot product can also be calculated by      A • B = Ax Bx + Ay By + Az Bz where vectors A and B are given as      A = Ax i + Ay j + Az k      B = Bx i + By j + Bz k Applications of the Dot Product Component Parallel to a Line Component Perpendicular to a Line Using the dot product, the angle between two known vectors A and B, can be determined as If the direction of a line is defined by the unit vector u, then the scalar component of the vector A parallel to that line is given by      A|| = A • u The vector component parallel to that line is given by      A|| = (A • u) u Using the properties of vector addition, or the Pythagorean theorem, we can also determine the scalar and vector components of A perpendicular to the line:  Practice Homework and Test problems now available in the 'Eng Statics' mobile app
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