1. ME221Lecture 61 ME 221 Statics Sections 2.6 – 2.8

2. ME221Lecture 62 Announcements HW #2 due Wednesday 9/10 2.22, 2.23, 2.25, 2.27, 2.29, 2.32, 2.37, 2.45, 2.47 & 2.50 Quiz #2 on Wednesday 9/10 Exam # 1 will be on Wednesday 9/17

3. ME221Lecture 63 Nonorthogonal Bases; Linear Equations Resolving vectors onto nonorthogonal directions Setting up and solving linear systems of algebraic equations Resolving Vectors into Components Using Angle Notation

4. ME221Lecture 64 Case 2: Two Directions Known Write out unit vectors x y P   P = A + B P = Pcosβ î + Psinβ ĵ

5. ME221Lecture 65 Write the components of P and write the vector sum equation Next, write the x and y component equations x-components y-components Here, we have two equations in two unknowns, A and B. Solve the equations.

6. ME221Lecture 66 The example we used had numerical values: P = 100 lb,  = 10º,  = 20º Set up the system of equations to solve 93.97 = A + 0.866 B x-components 34.20 = 0 A + 0.5 B y-components Solving yields: B = 68.4 lb and A = 34.7 lb

7. ME221Lecture 67 Linear Algebraic Systems Write the x- and y-component equations in matrix form as follows: Solve with your calculator.

8. ME221Lecture 68 Summary Sections 2.6 – 2.7 Be able to resolve a vector onto non- orthogonal directions Write the matrix form of the x-, y-, and z- component equationsWrite the matrix form of the x-, y-, and z- component equations Be able to solve a 2 x 2 and 3 x 3 system of equations on your calculatorBe able to solve a 2 x 2 and 3 x 3 system of equations on your calculator

9. ME221Lecture 69 Multiplying Vectors Section 2.8 There are three basic ways vectors are multiplied –Scalar times a vector –Scalar product –Cross or vector product Often called the “dot” product

10. ME221Lecture 610 Dot Product Consider two vectors A and B with included angle   A B By definition, the dot product is A B = |A| |B| cos 

11. ME221Lecture 611 Dot Product of Base Vectors Let A and B be the base vectors and we find Also note that since  = 0, then cos  = 1 since  = 90°, then cos  = 0 ··· ···

12. ME221Lecture 612 Writing the Components The dot product between two vectors is: Components of a vector may be easily found And finally ·... ·.

13. ME221Lecture 613 Applications Determine the angle between two arbitrary vectors Components of a vector parallel and perpendicular to a specific direction · · · ||