Math233_FinalExam_TopicList_2019F.pdf - Math 233 Final Exam Study Guide The final exam will cover the following sections of the textbook 13.1 13.5 14.1

Math233_FinalExam_TopicList_2019F.pdf - Math 233 Final Exam...

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Math 233 Final Exam Study GuideThe final exam will cover the following sections of the textbook: 13.1 - 13.5, 14.1 - 14.4,15.1 - 15.7, 16.1 - 16.5, 17.1 - 17.4. Below is a list of topics covered.13-Dimensional Geometry and Quadric surfaces1. The right hand rule2. The distance formula3. The equation of a sphere4. Identify which equations correspond to which quadric surfaces, using tricks likesettingz=cfor some constant c in the original equation, identifying the curve(parabola, ellipse) that the resulting equation describes, and comparing this to thecurve you get by intersecting the quadric surface with the horizontal planez=c.The same technique can be used to setx=cin the equation and compare to theintersection of the quadric surface with the vertical planex=c. You do not need toknow the names of the surfaces.2VectorsSection 13.1, 13.2, 13.3, 13.45. Two points determine a vector by subtracting coordinates of the two points6. Vector addition, subtraction, and scalar multiplication using components7. Vector addition, subtraction, and scalar multiplication using arrows8. Length of a vector9. Finding unit vectors or vectors of a given length in the direction of another vector10. Writing vectors in terms of~i,~j,~k11. Physics problems using vectors to represent force or velocity and finding resultantforces or velocities12. Dot product - both definitions13. Properties of dot product (commutative, associative with scalar multiplication, dis-tributive)
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14. Find the angle between two vectors using the dot product.15. Dot product and perpendicular vectors16. Scalar and vector projection17. Find the components of a vector parallel to and normal to another vector, i.e. write~v=~p+~nwherepis parallel to some given vector~uand~nis perpendicular to~u18. Work is the dot product of the force vector and the displacement vector19. Cross product - both definitions20. Length and direction of cross product21. Cross product and parallel vectors22. Properties of cross product (anti-commutative, distributive, associative for scalarmultiplication together with vector cross product, but not for the cross product ofthree vectors)23. Applications of cross product: area of parallelogram, triangle. (You do not need toknow torque or volume of parallelpiped.)3Lines and PlanesSection 13.524. Vector equation, parametric equations, and symmetric equations of line through apoint, parallel to a vector25. Finding equation of a line through two points26. Equation of a line segment27. Determining if lines are parallel or perpendicular or skew28. Equation of a plane through a point with a give normal vector29. Finding equation of a plane through three points, or through a point and a line, etc.30. Finding the intersection of two planes, or a plane and a line, etc.31. Angle between two planes.32. Using scalar projection to find distances between two planes, or point and plane,etc. You do not need to memorize formulas for this.
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