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Vectors and Parametric Equations

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Vectors and Parametric Equations

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    1. Vectors and Parametric Equations Alex Bottiggi and Christa Johnson December 9th, 2004 Pre-Calculus

    2. Section 8-1 Geometric Vectors Adding and Subtracting Vectors Find the sum of A+B. This is possible by drawing a parallelogram with vectors A and B The resultant can also be found by drawing a triangle with the two vectors and using the Pythagorean Theorem to solve the sides.

    3. Section 8-1 Examples 1.) Find p-q 2.) Find horizontal and vertical components when p=10

    4. Section 8-2 Algebraic Vectors Find an Ordered pair that can Represent a Vector Find the ordered pair that represents the vector from A (3,1) to B (-7,4). Then find the magnitude of vector AB. AB = (-7-3, 4-1) = (-10,3) Magnitude of AB = v(-7-3)^2 + (4-1)^2 or v109

    5. Section 8-2 Examples Find the ordered pair that represents the vector from C to D. The find the magnitude of CD C (-6,4) D(-5,-4) Find an ordered pair to represent vector u in each equation if V = (2,-5) and W = (3,-1) u = v+w

    6. Section 8-3 Vectors in Three-Dimensional space Find the ordered triple that represents the vector from R (-2,0,8) to S (5,-4,-1). Write in terms of unit vectors. RS = (5-(-2), -4-0, -1-8) RS = (7, -4, -9) Unit Vector = 7i-4j-9k

    7. Section 8-3 Examples For each pair of points E and F, find an ordered triple that represents EF. Then write EF as a sum of unit vectors. E = (2,-1,4) and F = (6,-2,1) E = (9,8,5) and F = (-1,5,11)

    8. Section 8-4 Perpendicular Vectors Find the inner product of vectors a and b if Vector a = (3,-1,7) and b = (0,-2,-4) Multiply X values, Y values, and Z values, then add them together. 3(0) + (-1)(-2) + 7(-4) = -26 The inner product is -26. If the answer is 0, the vector is perpendicular. If the answer is not 0, then the vector is not perpendicular.

    9. Section 8-4 continued To find a cross product, you have to find the discriminant of the ordered triples that are given to you. (5,2,3) and (-2,5,0) i j k [ 5 2 3 -2 5 0] Multiply your answer to the discriminant to each row. If you get 0, then the vector is perpendicular.

    10. Section 8-4 Examples Find the inner product 1.) (5,-1) * (-2,6) Find the cross product 2.) (2,-1,4) x (6,-2,1)

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