As an engineering student who has just finished MATH 137 and registering for MATH 213 for the coming semester or returning to school and having to take MATH 213, thinking the class will be full of multidimensional so that you will be stuck in the space. Well, the good news is that you will be in a fixed concrete classroom. In MATH 213, you will learn many topics regarding lines, vectors, cones and so on. Among these topics, I would like to present a topic that is easy to understand, however, tricky to relate the concepts to non-context problem. The topic is called Dot Product of two vectors. The dot product of two vectors can be described as
There is also another equivalent and it can be described as
Where, theta is the angle between vector …show more content…
In the system, focusing on the block, there are two forces residing on the block, which are its weight and its normal force that keeps the block from freefalling. However, normal force is perpendicular to the direction of the block’s displacement resulting on work done by the normal force because cos (90) is zero. Therefore, finding the total energy of the system, there is only initial potential energy due to the block’s position relative to the ground in vertical direction.
According to Zavala & Barniol, (2013), a study was conducted at a private Mexican university, which tested 422 students who were completing introductory physics courses with three isomorphic multiple-choice problems. The test purpose was to study students’ understanding of the Dot Product. The outcomes was that only 21% of tested students selected the correct answer to non-context problem, and the percentage is relatively lower than the other two problems’ percentages: 39% and 32%. Figure 2 (flylib.com, …show more content…
The multiple choices were “ (a) the magnitude of a vector between A and B pointing up to the right, (b) a vector in the direction of B, (c) a vector in the direction of A, (d) a vector between A and B pointing up to the right, (e) the projection of vector A onto vector B multiplied by the magnitude of vector B,(f) a vector perpendicular to both vectors.” (Zavala & Barniol, 2013, p. 439) The question posted on non-context problem was that what choice make the best interpretation of the dot product (A.B), the second work problem had a question asking which option would interpret the best the dot product of work, (W=F. d); the third electric flux posted asking which choice best interpret the electric flux through the surface, defining this flux as the dot product (E. A) (Zavala & Barniol, 2013). The tantalizing correct answer to the problems is (e), which is the projection of a vector A onto vector B multiplied by the magnitude of vector B (Zavala & Barniol,
There is also another equivalent and it can be described as
Where, theta is the angle between vector …show more content…
In the system, focusing on the block, there are two forces residing on the block, which are its weight and its normal force that keeps the block from freefalling. However, normal force is perpendicular to the direction of the block’s displacement resulting on work done by the normal force because cos (90) is zero. Therefore, finding the total energy of the system, there is only initial potential energy due to the block’s position relative to the ground in vertical direction.
According to Zavala & Barniol, (2013), a study was conducted at a private Mexican university, which tested 422 students who were completing introductory physics courses with three isomorphic multiple-choice problems. The test purpose was to study students’ understanding of the Dot Product. The outcomes was that only 21% of tested students selected the correct answer to non-context problem, and the percentage is relatively lower than the other two problems’ percentages: 39% and 32%. Figure 2 (flylib.com, …show more content…
The multiple choices were “ (a) the magnitude of a vector between A and B pointing up to the right, (b) a vector in the direction of B, (c) a vector in the direction of A, (d) a vector between A and B pointing up to the right, (e) the projection of vector A onto vector B multiplied by the magnitude of vector B,(f) a vector perpendicular to both vectors.” (Zavala & Barniol, 2013, p. 439) The question posted on non-context problem was that what choice make the best interpretation of the dot product (A.B), the second work problem had a question asking which option would interpret the best the dot product of work, (W=F. d); the third electric flux posted asking which choice best interpret the electric flux through the surface, defining this flux as the dot product (E. A) (Zavala & Barniol, 2013). The tantalizing correct answer to the problems is (e), which is the projection of a vector A onto vector B multiplied by the magnitude of vector B (Zavala & Barniol,