Geometry Lesson 8 7 Vectors Objective Find magnitudes

Geometry Lesson 8 – 7 Vectors Objective: Find magnitudes and directions of vectors. Add and subtract vectors.

Vector A quantity that has both magnitude and direction. What is magnitude? l The length of the vector from its intial point to its terminal point. What is direction? l The angle that is formed with the x-axis or any other horizontal line.

Vector

Standard position A vector is standard position when its initial point is at the origin.

Component Form Described in terms of its horizontal change x and vertical change y from initial point to terminal point. Component form:

Write the component form of CD What is the change in x? What is the change in y?

Write the component form of vector PQ.

Find the magnitude and direction of vector RT for R (2, 4) and T(-3, -2) Magnitude same as length same as distance. How do we find distance? Cont…

Find direction: Graph vector. Cont…

Direction is the angle the vector makes with the positive x axis. Reposition the vector so that it is on the origin. So vector RT has a Magnitude of 7. 8 units And a direction of about 230. 2 degrees.

Find the magnitude and direction. Cont…

Direction 54. 5 270 + 54. 5 = 324. 5 Magnitude is 8. 6 units, direction about 324. 5 degrees.

Vector Addition Equal vectors l Two vectors are equal if and only if they have the same magnitude and direction. Parallel vectors Two vectors are parallel if and only if they have the same or opposite direction. l Opposite vectors l Two vectors are opposites if they have the same magnitude and opposite directions.

Vector Addition: Parallelogram Method Step 1 l Place both vectors at the same initial point. Step 2 Complete the parallelogram. l The resultant is the diagonal of the parallelogram. l

Step 1 l Vector Addition: Triangle Method Place the initial point of the second vector at the terminal point of the first. Step 2 l The resultant connects the initial point of the first vector and the terminal point of the second.

Vector Addition and Subtraction. Find

Vector Addition and Subtraction. Find Subtracting a vector is like Adding its opposite.

Vector Addition and Subtraction. Find

Vectors can be added algebraically.

Cheerleaders are using an air launcher to project Tshirts into the stands. The wind is blowing in the same direction that the shirts are launched. If a shirt leaves the launcher at 40 feet per second at an angle of 45 o and the wind is blowing 7 feet per second parallel to the horizontal, what is the resultant velocity and direction of the T-shirt? Cont…

Add 7 for wind