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Chapter 5 Activities A NAME: 5.1 Adding “tip to tail” Assignment 1 06 points New Vector, negative Vector, Magnitude 10 points Describe the zero vector: 03 points Adding vectors tip to tail #2 06 points 5.2 #1, which symbol? 03 points Representing Vectors as Coordinates 08 points More practice, with algebra and sketches 06 points 5.3 How many dimensions 03 points A23 03 points It doesn’t commute! 06 points Solving the new Way 10 points Matrix Form 06 points 1 5.1 Vectors as Oriented Line Segments Adding “tip to tail” Assignment 1 V1 with (1, 1) base to (2, 2) tip and V2 with (1,3) base and (3, 5) tip. What is the resultant vector? How long is it and what are the coordinates of the tip and the tail? Remind me to talk to you about this part now! 2 New Vector, negative Vector, Magnitude Sketch the vector with (1, 1) as it’s tail and (5, 7) as it’s tip. Call it AB . Which point goes with the letter A and which point goes with the letter B? Find the magnitude: AB see page 165 3 Find − AB Describe this vector: Find a vector with it’s tail at the origin that has the SAME magnitude, call it OP . Is it true that AB = OP ? Read the book: page 163 before you answer! 4 5.1 continued Describe the zero vector: Sketch the zero vector: Why do you suppose we care about a zero vector. Starts with a G. one syllable. 5 Adding vectors tip to tail #2 Given A, a vector from (1, 0) to (3, 4) and B, a vector from (0, 2) to (5, 7) Add A + B to get resultant vector R What are some point coordinates for R? What are some point coordinates for a vector equal to R? What is the norm of R? 6 5.2 Representing Vectors with Coordinates A. Sketch (0,0) to (5, 3) Represent it as a column vector. Using which set of symbols? 7 Representing Vectors as Coordinates 2 08 points 1 Given A = and B = Find A + B. Show your work! 6 3 8 More practice, with algebra and sketches Given A = (−1, 5) and B = (3, 7) find 3 OA − 2 OB , give the matrix resultant tip and sketch the resultant vector. Algebra: Sketch: 9 Starting into 5.3 How many dimensions do we have here and 1 what does the vector 2 look like? 1 10 It doesn’t commute: Pick two 2 x 2 matrices and demonstrate that matrix multiplication does not commute. You may put in a zero and a one in each matrix…not more, though. 11 A23 Fill in a 3 x 3 matrix with numbers and then circle a23 12 Solving for the intersection in the Cartesian Plane The new way 5x + 2y = 11 4x + y = 7 13 Write the problem in MATRIX form 2x + 5 y = 1 3x + y = –5 Hint: matrix form is AX = B and stop. 14
