![]() ![]() Therefore, if the angle between the two vectors is zero, meaning that the two vectors are in the same direction, then the cosine of zero is equal to one. ![]() This value is the magnitude of V3 times the projection of V3 onto itself.Īn additional definition of the dot product is the magnitude of one vector times the magnitude of another vector times cosine of the angle between the two vectors. Therefore, the dot product of V3 and V3 is 11. Finding the dot product of the same two vectors (meaning they both have the same magnitude and same direction) is found the exact same way. For example the dot product of A and B is the magnitude of A times the projection of B onto A. ![]() These resulting scalar numbers represent one vector’s magnitude times the other vector’s projection onto the first vector. The same concept is used for finding the dot product of V3 and V4, which resulted to be 3. Multiply the x, y, and z components: (V2x*V3x= 3, V2y*V3y=2, V2z*V3z=1) The dot product of V2 and V3 resulted in 6. The dot product is determined by multiplying the x, y, and z-components of one vector by the x, y, and z-components of the other vector, and then adding up the three numbers together. The dot product of two vectors results in a scalar. By applying our knowledge of mathematics, this lab should assist us in solving real world problems in a simpler manner. Using Mathematica we can evaluate infinite series and to evaluate infinite sums. We will learn to graph many different types of surfaces, as well as solve complicated real life problems. We will also be able to use and apply Mathematica’s graphing capabilities. These commands include NSolve, Integrate, Simplify, and many more. The purpose of the lab allows for us to become familiar with the numerous commands of Mathematica. This program will allow us to demonstrate the properties of dot products versus cross products. We will further expand our knowledge of vectors by using the Mathematica program. In this lab we will use Mathematica to perform many mathematical operations.
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