PPT-A new way of multiplying two vectors is introduced in this

Dot Product Scalar Product Tensor Product Cross Product Angular Product A new way of multiplying two vectors is introduced in this chapter What is it called Dot Product Scalar Product. 1 Motivation A3 A2 Vectors A3 A21 Notational Conventions A4 A22 Visualization A5 A23 Special Vectors A5 A3 Vector Operations A5 A31 Transposition A6 A32 Equality A6 A33 Addition and Subtraction A.S. 1.3.1 – 1.3.4. Scalar Quantities. Those values, measured or coefficients, that are complete when reported with only a magnitude. Examples:. . the table is 2.5 m long. . He ran the 100. m race in 12.65 s.. Objectives. :. Distinguish between vector and scalar quantities. Add vectors graphically. Scalar. – a quantity that can be completely described by a number (called its magnitude) and a unit.. Ex: length, temperature, and volume. At the end of yesterday, we addressed the case of using the dot product to determine the angles between vectors. Similar to equations from algebra, we can talk about relationship of vectors as well. Parallel. Any vector can be resolved into horizontal and vertical components. v. v. x. v. y. A Helicopter is traveling . above a highway at . 29m/s at an angle of 25 degrees with respect to flat ground.. . How fast would a sports car have to travel to stay beneath the helicopter?. . example:. ..  .  .  . where . are unit vectors in x, y and z directions..  . .  .  .  .  . Both, position vector of point A and point A have the same coordinates:. Vector as position vector of point A in . . Vectors. . . . When an object moves along a straight line, its velocity can be determined by a single number that represents both magnitude and direction. (forward if positive and backward if negative.. Scalar. A . SCALAR. is ANY quantity in physics that has . MAGNITUDE. , but NOT a direction associated with it.. Magnitude. – A numerical value with units.. Scalar Example. Magnitude. Speed. 20 m/s. Any vector can be resized by multiplying it by a real number (scalar).. Multiplying by positive scalar changes magnitude only.. Multiplying by a negative scalar changes the magnitude and its direction.. SOL A.2b. REVIEW. Represent . Polynomials Using Algebra . Tiles. Represent x. 2. 3. 2) Represent x. 2. 4x – 2. . REVIEW. Represent . Polynomials Using Algebra . Tiles. 3) Represent 3x. Chapter 3 pg. . 81-105. What do you think?. How are measurements such as mass and volume different from measurements such as velocity and acceleration?. How can you add two velocities that are in different directions?. 1. Remember that fractions are parts of a whole or a part of a set of objects. For example, if a bag of apples contains 10 apples and three of the apples are used to make apple tarts, three-tenths, 3/10, of the apples have been used and seven-tenths, 7/10, of the original set of 10 apples remain. . Multiplying Decimals Example: 5.63 x 3.7 5 . 63 3 . 7 x 1 2 4 4 39 0 9 8 1 16 + 1 3 1 8 1 0 1 2 two one three . You do not line up the factors by the decimal. Instead, place the number with more digits on top. Slides 13-15: . Workbook Introduction Problem p. 55 . Slide 16: . Workbook Practice. . p. 57-58. Multiplying Multi-Digit Numbers. Enhanced Learning Task. What do we know?. . What do we need to find?.