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
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 Winter '11
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 Calculus, Vectors, Tier One, Scaled Composites, different direction, Plane Vectors

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