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4.7 Vectors in the Plane

# 4.7 Vectors in the Plane - Vectors in the Plane Vectors in...

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Unformatted text preview: Vectors in the Plane Vectors in the Plane Section 4.7 Quantities that have magnitude (length) and direction are called vectors. u Same magnitude, v Different direction u = v Same direction, Different magnitude, Different Different direction If a vector is placed on a standard coordinate plane with its tail, or initial point, at the origin, the vector is said to be in standard position. y x B Terminal point A Initial point → AB = ( x2 − x1 ) 2 + ( y2 − y1 ) 2 The norm or magnitude (length) of a vector is v represented by and is found by using the distance formula. v = a, b v = a +b 2 2 The sum, or resultant, of two vectors is also a vector. Vectors u and v can be added using parallelogram addition or tail­to­head addition. Each method yields the same resultant vector w. v w + v = u u If u = 5, 2 and v = 1,3 u + v = 6,5 u + v w = u v The direction angle is the measure of the angle between the vector and the positive x­axis. y C (a, b) v θ b a x b = sin θ v a = cos θ v b = v sin θ a = v cos θ Joke Time Joke Time What starts with P, ends with E, and has thousands of letters in it? Post Office Forwards it is heavy, backwards it is not. What is it? A ton What music do mummies like? Wrap music ...
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