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Unformatted text preview: Name: ______________________________________ Date: ________________________ Student Exploration: Vectors Vocabulary: component, dot product, magnitude, resultant, scalar, unit vector notation, vector Prior Knowledge Question (Do this BEFORE using the Gizmo.) An airplane is traveling north at 300 km/h. Suddenly it is hit by a strong crosswind blowing 150 km/h from west to east. Draw an arrow on the diagram showing the direction you think the plane will most likely move. Explain your answer. __________________________________________________ __________________________________________________ Gizmo Warm-up Displacement, velocity, momentum, acceleration, and force are all examples of quantities that have both direction and magnitude . Anything with direction and magnitude can be represented using a vector . Look at vectors a and b on the Vectors Gizmo grid. The initial point of each vector is shown with a circle. The terminal point of each vector is located at the tip of the arrow. Each vector is described by two components : the i component and the j component. 1. The two components written together make up the unit vector notation . What is the unit vector notation of vector a ? ___________________________________________________ 2. Move the initial point of vector a to the origin (0, 0) on the grid. A. How did the components of vector a change? _______________________________ B. Drag the terminal point of vector a so that it lines up with the x-axis. Which component describes the vectors position along the x-axis? ___________________ C. Drag the terminal point of a so that it lines up with the y-axis. Which component describes the vectors position along the y-axis? ____________________________ Activity A: Vector magnitude and angle Get the Gizmo ready : Change vector a so that its notation is 0 i + 3 j . You will need a scientific calculator for this activity. Question: How can you determine a vectors magnitude and angle? 1. Observe : The magnitude of a vector is the distance from the vectors initial point to its terminal point. The magnitude of a vector is written: || x ||. Magnitude is a scalar , or a number that does not indicate direction. A. What is the magnitude of vector a ? || a || = ______________ Turn on Click to measure lengths and use the ruler to check your answer. B. Turn off the Ruler . Drag the tip of vector a so that its notation is 4 i + 3 j . What do you think the magnitude of vector a is now? || a || = ______________ 2. Explore : A vector can be broken down into perpendicular vectors that describe its length along the x and y axes. Turn on Show x, y components . How do the x and y vectors that appear for vector a relate to the i and j notation?...
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- Spring '11