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1. Draw the components of each vector in the following diagrams. Then calculate the length of each component. a) b) 23° 2. For each of the following, draw the given vectors tip to tail, draw the resultant vector including angle, then calculate the magnitude and direction of the resultant vector. a) I travel 17m West, then 14m South.
Vector quantity: quantity with a magnitude and a direction. It can be represented by a vector. Examples: displacement, velocity, acceleration. Same displacement. Displacement does not describe the object’s path.
The tool displays a coordinate plane with a grid of 10 square units. Click anywhere in the grid to create a blue vector, then click again to create a red vector. As you click or drag, the tool calculates the components, magnitude, and direction of the vectors.
Find the unit vector in the direction of sum of two vectors ⃗ v = (2, −4) and ⃗w = (−3, 2). Solution: the sum of two given vectors, we call it ⃗c, is calculated as below. ⃗c = ⃗v + ⃗w = (2, −4) + (−3, 2) = (2 + (−3), −4 + 2) = (−1, −2) The magnitude of this vector is also found as √. ⃗c| = p(−1)2 + (−2)2 = 5.
The magnitude of C~ = ABsin˚ Discuss the right-hand rule and right-handed coordinate systems. Do some examples. Exercise 1.45 For the two vectors A~and D~ in Fig. E1.22 (see the gure above), a) nd the magnitude and direction of the vector product A~ D~; b) nd the magnitude and direction of D~ A~.
For each vector drawn below, calculate its magnitude and direction. NOTE: For the vector’s direction, there will be two possible correct answers for each problem.
Find the component form, magnitude, and direction angle for the given vector 9) CD where C = ( , ) D = ( , ) Sketch a graph of each vector then find the magnitude and direction angle.
