SlideShare a Scribd company logo
1 of 1
Precalculus
8-3    Vectors in Three-Dimensional Space

   •  A 3-D coordinate grid has _________________ axes:
              __________________________________________________
   • A point in 3-D is represented by an ____________________________________.
   Find and plot the point (-4, 3, 2)




   Graph the vector 5, −2,14




   Representing a vector as an ordered triple:
          Initial:       P1(x1, y1, z1)
          Terminal:      P2(x2, y2, z2)

                                         r     ρ    r               r
Find an ordered triple that represents 3 p − 2 θ if p = 3, 0, 4 and q = 2,1,−1 .




Unit Vectors: ____________________________________________________________
Write AB as the sum of unit vectors for A(5, 10, -3) and B(-1, 4, -2).




HW p. 503 (16 – 34 even)

More Related Content

What's hot

A28 1 exp growth no
A28 1 exp growth noA28 1 exp growth no
A28 1 exp growth no
vhiggins1
 
4.3 intercepts
4.3 intercepts4.3 intercepts
4.3 intercepts
vhiggins1
 
G6 m3-c-lesson 15-s
G6 m3-c-lesson 15-sG6 m3-c-lesson 15-s
G6 m3-c-lesson 15-s
mlabuski
 
Derivative investigation
Derivative investigationDerivative investigation
Derivative investigation
jchartiersjsd
 
A26-6 poly zeros notes
A26-6 poly zeros notesA26-6 poly zeros notes
A26-6 poly zeros notes
vhiggins1
 
7th math c2 -inv#3
7th math c2 -inv#37th math c2 -inv#3
7th math c2 -inv#3
jdurst65
 
8 1 zero and negative exponents-modified
8 1 zero and negative exponents-modified8 1 zero and negative exponents-modified
8 1 zero and negative exponents-modified
chrystal_brinson
 
2 3 graphing polynomials
2 3 graphing polynomials2 3 graphing polynomials
2 3 graphing polynomials
hisema01
 
6.4 Graphing Polynomials (Relative Max/Min, Zeros)
6.4 Graphing Polynomials (Relative Max/Min, Zeros)6.4 Graphing Polynomials (Relative Max/Min, Zeros)
6.4 Graphing Polynomials (Relative Max/Min, Zeros)
swartzje
 
Xmss ict lesson sec 2 qe wksheet
Xmss  ict lesson sec 2 qe wksheetXmss  ict lesson sec 2 qe wksheet
Xmss ict lesson sec 2 qe wksheet
bryan
 

What's hot (20)

Prac 2 rolle's thm
Prac  2 rolle's thmPrac  2 rolle's thm
Prac 2 rolle's thm
 
A28 1 exp growth no
A28 1 exp growth noA28 1 exp growth no
A28 1 exp growth no
 
Class notes for discovering transformation of the parent graph for the square...
Class notes for discovering transformation of the parent graph for the square...Class notes for discovering transformation of the parent graph for the square...
Class notes for discovering transformation of the parent graph for the square...
 
4.3 intercepts
4.3 intercepts4.3 intercepts
4.3 intercepts
 
1 13s-f
1 13s-f1 13s-f
1 13s-f
 
G6 m3-c-lesson 15-s
G6 m3-c-lesson 15-sG6 m3-c-lesson 15-s
G6 m3-c-lesson 15-s
 
Prac 3 lagrange's thm
Prac  3 lagrange's thmPrac  3 lagrange's thm
Prac 3 lagrange's thm
 
Practice for Square Root Graph & Transformations
Practice for Square Root Graph & TransformationsPractice for Square Root Graph & Transformations
Practice for Square Root Graph & Transformations
 
Prac 4 integral as limit of sum
Prac  4  integral as limit of sumPrac  4  integral as limit of sum
Prac 4 integral as limit of sum
 
Derivative investigation
Derivative investigationDerivative investigation
Derivative investigation
 
precalc preTest 3
precalc preTest 3precalc preTest 3
precalc preTest 3
 
A26-6 poly zeros notes
A26-6 poly zeros notesA26-6 poly zeros notes
A26-6 poly zeros notes
 
7th math c2 -inv#3
7th math c2 -inv#37th math c2 -inv#3
7th math c2 -inv#3
 
Math 116 pres. 5
Math 116 pres. 5Math 116 pres. 5
Math 116 pres. 5
 
8 1 zero and negative exponents-modified
8 1 zero and negative exponents-modified8 1 zero and negative exponents-modified
8 1 zero and negative exponents-modified
 
2 3 graphing polynomials
2 3 graphing polynomials2 3 graphing polynomials
2 3 graphing polynomials
 
6.4 Graphing Polynomials (Relative Max/Min, Zeros)
6.4 Graphing Polynomials (Relative Max/Min, Zeros)6.4 Graphing Polynomials (Relative Max/Min, Zeros)
6.4 Graphing Polynomials (Relative Max/Min, Zeros)
 
Polynomial
PolynomialPolynomial
Polynomial
 
Xmss ict lesson sec 2 qe wksheet
Xmss  ict lesson sec 2 qe wksheetXmss  ict lesson sec 2 qe wksheet
Xmss ict lesson sec 2 qe wksheet
 
1-6 the coordinate plane part 2
1-6 the coordinate plane part 21-6 the coordinate plane part 2
1-6 the coordinate plane part 2
 

More from vhiggins1

A1 12 scatter plots
A1 12 scatter plotsA1 12 scatter plots
A1 12 scatter plots
vhiggins1
 
A1 11 functions
A1 11 functionsA1 11 functions
A1 11 functions
vhiggins1
 
A1 11 functions
A1 11 functionsA1 11 functions
A1 11 functions
vhiggins1
 
A2 Test 3 with answers 2011
A2 Test 3 with answers 2011A2 Test 3 with answers 2011
A2 Test 3 with answers 2011
vhiggins1
 
A1 Test 3 study guide with answers
A1 Test 3 study guide with answersA1 Test 3 study guide with answers
A1 Test 3 study guide with answers
vhiggins1
 
PC Test 2 study guide 2011
PC Test 2 study guide 2011PC Test 2 study guide 2011
PC Test 2 study guide 2011
vhiggins1
 
A2 Test 2 study guide with answers (revised)
A2 Test 2 study guide with answers (revised)A2 Test 2 study guide with answers (revised)
A2 Test 2 study guide with answers (revised)
vhiggins1
 
A2 Test 2 study guide with answers
A2 Test 2 study guide with answersA2 Test 2 study guide with answers
A2 Test 2 study guide with answers
vhiggins1
 
A1 Test 2 study guide with answers 2011
A1 Test 2 study guide with answers 2011A1 Test 2 study guide with answers 2011
A1 Test 2 study guide with answers 2011
vhiggins1
 
A1 Test 2 study guide
A1 Test 2 study guideA1 Test 2 study guide
A1 Test 2 study guide
vhiggins1
 
PCExam 1 practice with answers
PCExam 1 practice with answersPCExam 1 practice with answers
PCExam 1 practice with answers
vhiggins1
 
PCExam 1 study guide answers
PCExam 1 study guide answersPCExam 1 study guide answers
PCExam 1 study guide answers
vhiggins1
 
PC Exam 1 study guide
PC Exam 1 study guidePC Exam 1 study guide
PC Exam 1 study guide
vhiggins1
 
PC 1 continuity notes
PC 1 continuity notesPC 1 continuity notes
PC 1 continuity notes
vhiggins1
 
PC 1 continuity
PC 1 continuityPC 1 continuity
PC 1 continuity
vhiggins1
 
A1 3 linear fxns
A1 3 linear fxnsA1 3 linear fxns
A1 3 linear fxns
vhiggins1
 
A1 3 linear fxns notes
A1 3 linear fxns notesA1 3 linear fxns notes
A1 3 linear fxns notes
vhiggins1
 
A1 2 linear fxns
A1 2 linear fxnsA1 2 linear fxns
A1 2 linear fxns
vhiggins1
 
A1 2 linear fxns notes
A1 2 linear fxns notesA1 2 linear fxns notes
A1 2 linear fxns notes
vhiggins1
 
A2 2 linear fxns notes
A2 2 linear fxns notesA2 2 linear fxns notes
A2 2 linear fxns notes
vhiggins1
 

More from vhiggins1 (20)

A1 12 scatter plots
A1 12 scatter plotsA1 12 scatter plots
A1 12 scatter plots
 
A1 11 functions
A1 11 functionsA1 11 functions
A1 11 functions
 
A1 11 functions
A1 11 functionsA1 11 functions
A1 11 functions
 
A2 Test 3 with answers 2011
A2 Test 3 with answers 2011A2 Test 3 with answers 2011
A2 Test 3 with answers 2011
 
A1 Test 3 study guide with answers
A1 Test 3 study guide with answersA1 Test 3 study guide with answers
A1 Test 3 study guide with answers
 
PC Test 2 study guide 2011
PC Test 2 study guide 2011PC Test 2 study guide 2011
PC Test 2 study guide 2011
 
A2 Test 2 study guide with answers (revised)
A2 Test 2 study guide with answers (revised)A2 Test 2 study guide with answers (revised)
A2 Test 2 study guide with answers (revised)
 
A2 Test 2 study guide with answers
A2 Test 2 study guide with answersA2 Test 2 study guide with answers
A2 Test 2 study guide with answers
 
A1 Test 2 study guide with answers 2011
A1 Test 2 study guide with answers 2011A1 Test 2 study guide with answers 2011
A1 Test 2 study guide with answers 2011
 
A1 Test 2 study guide
A1 Test 2 study guideA1 Test 2 study guide
A1 Test 2 study guide
 
PCExam 1 practice with answers
PCExam 1 practice with answersPCExam 1 practice with answers
PCExam 1 practice with answers
 
PCExam 1 study guide answers
PCExam 1 study guide answersPCExam 1 study guide answers
PCExam 1 study guide answers
 
PC Exam 1 study guide
PC Exam 1 study guidePC Exam 1 study guide
PC Exam 1 study guide
 
PC 1 continuity notes
PC 1 continuity notesPC 1 continuity notes
PC 1 continuity notes
 
PC 1 continuity
PC 1 continuityPC 1 continuity
PC 1 continuity
 
A1 3 linear fxns
A1 3 linear fxnsA1 3 linear fxns
A1 3 linear fxns
 
A1 3 linear fxns notes
A1 3 linear fxns notesA1 3 linear fxns notes
A1 3 linear fxns notes
 
A1 2 linear fxns
A1 2 linear fxnsA1 2 linear fxns
A1 2 linear fxns
 
A1 2 linear fxns notes
A1 2 linear fxns notesA1 2 linear fxns notes
A1 2 linear fxns notes
 
A2 2 linear fxns notes
A2 2 linear fxns notesA2 2 linear fxns notes
A2 2 linear fxns notes
 

Pc8-3 3D Vectors Notes

  • 1. Precalculus 8-3 Vectors in Three-Dimensional Space • A 3-D coordinate grid has _________________ axes: __________________________________________________ • A point in 3-D is represented by an ____________________________________. Find and plot the point (-4, 3, 2) Graph the vector 5, −2,14 Representing a vector as an ordered triple: Initial: P1(x1, y1, z1) Terminal: P2(x2, y2, z2) r ρ r r Find an ordered triple that represents 3 p − 2 θ if p = 3, 0, 4 and q = 2,1,−1 . Unit Vectors: ____________________________________________________________ Write AB as the sum of unit vectors for A(5, 10, -3) and B(-1, 4, -2). HW p. 503 (16 – 34 even)