Activity A: Get the Gizmo ready: Describing . Drag the initial points of both vectors to the origin. vectors . Drag the terminal point of a to (4, 0) and the terminal point of b to (0, -3). 1. Recall that all vectors have magnitude (length) and direction. Magnitude is a scalar, or a number that does not indicate direction. A. Use north, south, east, or west to give the direction of a = and b = . B. The expressions ||all and ||b| | represent the magnitudes of a and b, respectively. Find ||all and I|bl|. llall = 11bll = Select Show ruler to open the Gizmo rulers. Attach the "donuts" to the initial and terminal points of the vectors to check your answers C. The magnitude of a vector is always positive. Why do you think this is true? 2. With the initial point of a at the origin, drag the terminal point so a = . (Drag vector b out of the way for now.) A. How does the direction of a change? B. Create a right triangle on the grid to the right that has vector a as the hypotenuse. The legs of the right triangle co are the components of vector a. Label the legs of the triangle a and b, and the hypotenuse c. No a C. Use the Pythagorean Theorem (a2 + b2 = c?) to find the length of the hypotenuse, c. This is the magnitude of a. 2 3 4 3. The initial point of a vector is (-3, 1) and the terminal point is (2, -1). Sketch the vector on the grid to the right. Then find its magnitude to the nearest hundredth. Show your work. -3 -2 2 3 -2Gizmo Warm-up A vector is a representation of something with both size, or 4 magnitude, and direction. For example, a moving car can be -3 represented by a vector because the car has both speed (magnitude) a 2 and direction. b On a graph, vectors are represented by arrows. The base of the arrow -2 -1 2 3 is the initial point and the tip of the arrow is the terminal point. 1. Drag the initial point (the circle) of vector a to the origin. This vector is now said to be in standard position. Notice the components of a shown in brackets like this: <_ _>. What are the components of a? 2. Drag the initial point of vector a around. A. Does this change the components of a? B. Compare the coordinates of the initial and terminal points of a to its components. How can you find the components of vector a