EXAM 1 Outline - 9 Know how to find the line of...

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EXAM 1 Outline 1. Vectors in n-space. The basic operations of vector addition and scalar multiplication. 2. Length and unit vectors. 3. The dot product. The fundamental properties of the dot product: a. |v|^2 = v . v b. u is perpendicular to v if u times v = 0 c. u . v = |u||v| cos theta where theta is the angle between the vectors. 4. Know how to calculate a determinant by expansion of cofactors, and know the basic properties of determinants. 5. Know the parametric equation of a line in n-space. 6. Know how to calculate the cross product u x v of two vectors in 3-space. 7. Know the basic properties of the cross-product: a. U x v is perpendicular to both u and v b. If and u and v are nonzero factors then u is parallel to v if u x v = 0. c. |u x v| = |u||v|sin theta where theta is the angle between the vectors, and hence is the area of the parallelogram determined by u an v. 8. Know how to find the equation of a plane in 3-space
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Unformatted text preview: 9. Know how to find the line of intersection of two planes and the point of intersection of a line and a plane. 10. Know the definition of a parametric curve (path) in n-space. 11. Velocity and acceleration vectors. 12. The line tangent to a path c at a point p. 13. Know how to find the general position vector when the initial conditions and the acceleration vector are given. 14. (Proof) The criterion for an object to move at constant speed along a path in n-space 15. Know Kepler’s laws. 16. Know the general idea of a cylinder (circular, elliptic or parabolic) in 3-space and know the equations of spheres, ellipsoids, and paraboloids. 17. Know the definition of the open r-ball, B(po,r), around a point po in n-space 18. Know the definitions of a real-valued function f of n variables and the definition of a limit....
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