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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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This note was uploaded on 12/01/2011 for the course MATH 111 taught by Professor Stuff during the Winter '11 term at BYU.
 Winter '11
 stuff
 Calculus, Vectors

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