Lesson 10.6.  Find scalar products of two-space vectors  Prove or disprove generalizations about vector operations  Identify parallel and orthogonal.

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Presentation transcript:

Lesson 10.6

 Find scalar products of two-space vectors  Prove or disprove generalizations about vector operations  Identify parallel and orthogonal vectors  Represent scalar multiplication of two-space vectors graphically  Represent lines in a plane using vector equations.

 A vector w = is a scalar multiple of vector u = written w = ku iff there exists a real number k such that =  Nonzero vectors u and v are parallel iff there exists a real number t ≠ 0 st u = tv  Two vectors are parallel if they have the same or exactly opposite direction.  The line through P = that is parallel to the vector v = has the vector equation = t Where t may be any real number.

 The vector u begins a (3, -7) and ends at (-4, 8). The vector v = 6.6u is in standard position. Where does v begin and where does it end?  It is in standard position, so we know it begins at (0, 0)  Vector u =  V = 6.6  V =

 Tell whether the two given vectors are parallel and justify your answer.  and Yes, k = -6  [13, 17˚] and [5, 163˚] No, they are not opposite directions.

Give an example of a vector parallel to that also meets the following criteria.  Has opposite direction:  Has magnitude equal to 1:

 Identify three points on the line described by: When t = 0, (-1, 2) t=1, (3, -1) t = 2, (7, -4) Write in point-slope form: y – 2 = -3/4(x + 1) Write a vector equation for this line. = t

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