9.1 Part 2 Vectors Geometry

Objectives: Students will find the component form, magnitude and the direction of the vector You will be able to answer questions that have to do with graphing the vector, putting it into component form, and then finding the magnitude. Mastery is 80% or better on 5-min check and Indy work.

Pay attention: You will be able to answer questions that have to do with graphing the vector, putting it into component form, and then finding the magnitude. The next three examples are good practice and/or notes to have on the Quiz / Test.

Finding the magnitude of a vector You begin with an initial point to a terminal point given in terms of points, usually P and Q. You graph it as you would a ray. Initial point is P(0, 0). Terminal point is Q(-6, 3). Q(-6, 3) P(0, 0)

Write the component form Here you write the following Component Form =(x2 – x1, y2 – y1) (-6 – 0, 3 – 0) (-6, 3) is the component form. Next use the distance formula to find the magnitude. |PQ| = √(-6 – 0)2 + (3 – 0)2 = √62 + 32 = √36 + 9 = √45 ≈ 6.7 Q(-6, 3) P(0, 0)

Think..Ink…Share..White Board P(0, 2). Q(5, 4). You can start looking for component form and magnitude. NOTE THE INITIAL POINT IS P & TERMINAL POINNT IS Q

Write the component form Here you write the following Component Form =(x2 – x1, y2 – y1) (5 – 0, 4 – 2) (5, 2) is the component form. Next use the distance formula to find the magnitude. |PQ| = √(5 – 0)2 + (4 – 2)2 = √52 + 22 = √25 + 4 = √29 ≈ 5.4

CFU- White Board P(3, 4). Q(-2, -1). Find the Component & Magnitude.

Write the component form Here you write the following Component Form =(x2 – x1, y2 – y1) (-2 – 3, -1 – 4) (-5, -5) is the component form. Next use the distance formula to find the magnitude. |PQ| = √-2 – 3)2 + (-1– 4)2 = √(-5)2 + (-5)2 = √25 + 25 = √50 ≈ 7.1

Adding Vectors Two vectors can be added to form a new vector. To add u and v geometrically, place the initial point of v on the terminal point of u, (or place the initial point of u on the terminal point of v). The sum is the vector that joins the initial point of the first vector and the terminal point of the second vector. It is called the parallelogram rule because the sum vector is the diagonal of a parallelogram. You can also add vectors algebraically.

What does this mean? Adding vectors: Sum of two vectors The sum of u = (X1,Y1) and v = (X2, Y2) is u + v = (X1 + X2, Y1 + Y2) In other words: add your x’s to get the coordinate of the first, and add your y’s to get the coordinate of the second.

Example: Find the sum Let u = (3, 5) and v = (-6, -1) To find the sum vector u + v, add the x’s and add the y’s of u and v. u + v = (3 + (-6)), 5 + (-1)) = (-3, 4)

What was the objective?: Students will find the component form, magnitude and the direction of the vector You will be able to answer questions that have to do with graphing the vector, putting it into component form, and then finding the magnitude. Mastery is 80% or better on 5-min check and Indy work.

HW Page 576 14-29 & 32