4_Vectors

# 4_Vectors - goes through the point (-2,4). Vector B has a...

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Vectors 3D Coordinate System Graph P(2, 4, -2) and Q(-3, 0, 5)

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A vector is a quantity specified by magnitude and direction. A scalar is a quantity specified by magnitude only. Geometric Vectors are represented by an arrow. Operations r u + r v
- v u v u - r v 2 r u - r u + 3 r v **** Two vectors are parallel if they are scalar multiples of each

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other.***** r u r v r u = c v v , c is a nonzero constant. If c > 0, the vectors go in the same direction. If c < 0, the vectors go in the opposite direction. i is the unit vector in the positive x direction. j is the unit vector in the positive y direction. PQ = q 1 - p 1 ( 29 i + q 2 - p 2 ( 29 j = q 1 - p 1 , q 2 - p 2
ex. The magnitude of v, r v o r r v = v 1 2 + v 2 2 . A unit vector is a vector of length 1. u = v v A vector is a product of magnitude and direction.

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v = v v v Direction is a UNIT vector. Algebraic addition: ex. Find the horizontal and vertical components of v if v has magnitude 3 and makes an angle of 20 degrees with the horizontal. ex. From an old EF test:
Vector A has a magnitude of 24.3 N, begins at the point (0,0) and

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Unformatted text preview: goes through the point (-2,4). Vector B has a magnitude of 13.8 N, begins at point (1, -2), and goes through the point (2, -1). Find the resultant vector A + B. Do: 1. Force A has a magnitude of 20 N and points in a direction of 150 degrees from the positive x axis. Force B has a magnitude of 6 N at an angle of 225 degrees. What is the resultant force A + B? 2. Suppose P(1, 2, 3) and Q(5, 0, -1). Find QP . 3D k is the unit vector in the positive z direction. PQ = q 1-p 1 ( 29 i + q 2-p 2 ( 29 j + q 3-p 3 ( 29 k = q 1-p 1 , q 2-p 2 , q 3-p 3 r v o r r v = v 1 2 + v 2 2 + v 3 2 ex. P(7, 1, 1) Q(0, 2, 3) Do: u = 2 ,-1 , 4 , v = 1 , 3 , 4 , w =-1 , 1 2 , 2 1. Find 2 u-v . 2. Find a vector of length 3 in the same direction as v . 3. Are any vectors parallel? 4. Find point B if A(1, 3), AB = 10 , AB 3 , 4 ....
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## This note was uploaded on 04/12/2008 for the course MATH 1224 taught by Professor Dontremember during the Fall '08 term at Virginia Tech.

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4_Vectors - goes through the point (-2,4). Vector B has a...

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