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mthsc206-fall-2010-exam-study-guide-01 - MthSc 206 Topics...

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Unformatted text preview: MthSc 206 Topics - Exam 1 1 Vectors • What two attributes does a vector possess? How is a vector different from a scalar? • Given two points P and Q , define the displacement vector v . • Given two vectors bfv and w (having the same dimension) and two scalars α and β , define (a) v + w ; (b) α v ; (c) v- w ; (d) α v + β w ; (e) || v || ; (f) v · w ; (g) v × w ; (h) || α v || . • How do you compute the angle between two vectors? • What is the algebraic description of the direction of a vector v ? • How do you show two vectors are perpendicular to one another? • How do you show two nonzero vectors are parallel to one another? • Define the vector projection of b onto a , i.e., proj a b . • What is the scalar component of the vector projection of v onto u , i.e., comp u v ? • What are some uses of vector projections? • How do you find the work done by a force F in moving an object along a straight line from a point P ( x , y , z ) to a point Q ( x 1 , y 1 , z 1...
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