This is not the document you are looking for? Use the search form below to find more!

0.00 (0 votes)

Lesson 2: Vectors and the Dot Product

- Added:
**April, 25th 2011** - Reads:
**241** - Downloads:
**0** - File size:
**287.12kb** - Pages:
**39** - content preview

- Name:
**shaiming**

Related Documents

Type 2 Diabetes and the USDA Dietary Guidelines

Dewalt DC740KA 12v Professional Drill Driver, 2 Batteries and Carry Case Click Here More ...

Watch Alvin and the Chipmunks 2 online free

DEAR SIR & MADAM : Avalon Rangoli ( DHARUHER ) 2 BHK and 3 BHK Apartments "After successful delivery of Avalon Gardens & launch of Residency (Phase-I & Phase-II), Avalon Homes, ...

watch Night and the City free online, watch Night and the City online

Booq Taipan Shadow XS And The Taipan Sneak XS Bags For Apple iPad- David Novak (TheGadgetGUYcolumn.com)

Harry Potter and the Philosopher's Stone by J. K. Rowling. A teachers' study guide

Everything you need to know about Harry Potter and the Order of the Phoenix

This guide covers Harry Potter and the Prisoner of Azkaban for the PC. The PC version of the game is radically different from the version released on the various consoles (PS2, Xbox, GameCube and ...

Pine Bend and The Hamptons at Pine Bend Apartments for Rent Brochure Mobile, AL

Content Preview

Section 9.2–3Vectors and the Dot ProductMath 21aFebruary 6, 2008AnnouncementsThe MQC is open: Sun-Thu 8:30pm–10:30pm, SC 222Homework for Friday 2/8:Section 9.2: 4, 6, 26, 33, 34Section 9.3: 10, 18, 24, 25, 34Section 9.4: 1*OutlineVectorsAlgebra of VectorsComponentsStandard basis vectorsLengthThe Dot ProductWorkConceptPropertiesUsesWhat is a vector?DeﬁnitionA vector is something that has magnitude and directionWe denote vectors by boldface (v) or little arrows (v ). One isgood for print, one for scriptGiven two points A and B in ﬂatland or spaceland, the vectorwhich starts at A and ends at B is called the displacement−→vector AB.Two vectors are equal if they have the same magnitude anddirection (they need not overlap)BDvuACscalarvectorvectorscalarVector or scalar?DeﬁnitionA scalar is another name for a real number.ExampleWhich of these are vectors or scalars?(i) Cost of a theater ticket(ii) The current in a river(iii) The initial ﬂight path from Boston to New York(iv) The population of the worldVector or scalar?DeﬁnitionA scalar is another name for a real number.ExampleWhich of these are vectors or scalars?(i) Cost of a theater ticket scalar(ii) The current in a river vector(iii) The initial ﬂight path from Boston to New York vector(iv) The population of the world scalarVector additionDeﬁnitionIf u and v are vectors positioned so the initial point of v is theterminal point of u, the sum u + v is the vector whose initial pointis the initial point of u and whose terminal point is the terminalpoint of v.uvvu + vu + vvuuThe triangle lawThe parallelogram lawOpposite and diﬀerenceDeﬁnitionGiven vectors u and v,the opposite of v is the vector −v that has the same lengthas v but points in the opposite directionthe diﬀerence u − v is the sum u + (−v)vu−vu − v2v− 1 v2Scaling vectorsDeﬁnitionIf c is a nonzero scalar and v is a vector, the scalar multiple cv isthe vector whoselength is |c| times the length of vdirection is the same as v if c > 0 and opposite v if c < 0If c = 0, cv = 0.v− 1 v2Scaling vectorsDeﬁnitionIf c is a nonzero scalar and v is a vector, the scalar multiple cv isthe vector whoselength is |c| times the length of vdirection is the same as v if c > 0 and opposite v if c < 0If c = 0, cv = 0.2vv2vScaling vectorsDeﬁnitionIf c is a nonzero scalar and v is a vector, the scalar multiple cv isthe vector whoselength is |c| times the length of vdirection is the same as v if c > 0 and opposite v if c < 0If c = 0, cv = 0.v− 1 v2Document Outline

- Announcements
- Vectors
- Algebra of Vectors
- Components
- Standard basis vectors
- Length

- The Dot Product
- Work
- Concept
- Properties
- Uses

## Add New Comment