Math Precalculus Vectors Vectors word problems Vector word problems CCSS.Math: HSN.VM.A.3 Google Classroom Facebook Twitter Email Vectors word problems Vectors word problem: pushing a box Vectors word problem: tug of war Vectors word problem: hiking Practice: Vector word problems This is the currently selected item.
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The sides of the right triangle have lengths of 11 km and 11 km. The resultant can be determined using the Pythagorean theorem; it has a magnitude of 15.6 km. The solution is shown below the diagram. Vector Problems With Solutions Plus A HypotenuseA right triangle has two sides plus a hypotenuse; so the Pythagorean theorem is perfect for adding two right angle vectors. But there are limits to the usefulness of the Pythagorean theorem in solving vector addition problems. For instance, the addition of three or four vectors does not lead to the formation of a right triangle with two sides and a hypotenuse. So at first glance it may seem that it is impossible to use the Pythagorean theorem to determine the resultant for the addition of three or four vectors. Furthermore, the Pythagorean theorem works when the two added vectors are at right angles to one another - such as for adding a north vector and an east vector. Vector Problems With Solutions How To Approach MoreBut what can one do if the two vectors that are being added are not at right angles to one another Is there a means of using mathematics to reliably determine the resultant for such vector addition situations Or is the student of physics left to determining such resultants using a scaled vector diagram Here on this page, we will learn how to approach more complex vector addition situations by combining the concept of vector components (discussed earlier ) and the principles of vector resolution (discussed earlier ) with the use of the Pythagorean theorem (discussed earlier ). The construction of a diagram like that below often proves useful in the visualization process. As can be seen in the diagram, the resultant vector (drawn in black) is not the hypotenuse of any right triangle - at least not of any immediately obvious right triangle. But would it be possible to force this resultant vector to be the hypotenuse of a right triangle The answer is Yes To do so, the order in which the three vectors are added must be changed. The vectors above were drawn in the order in which they were driven. But if the three vectors are added in the order 6.0 km, N 2.0 km, N 6.0 km, E, then the diagram will look like this. The lengths of the perpendicular sides of the right triangle are 8.0 m, North (6.0 km 2.0 km) and 6.0 km, East. The magnitude of the resultant vector (R) can be determined using the Pythagorean theorem. ![]() The size of the resultant was not affected by this change in order. This illustrates an important point about adding vectors: the resultant is independent by the order in which they are added. Adding vectors A B C gives the same resultant as adding vectors B A C or even C B A. As long as all three vectors are included with their specified magnitude and direction, the resultant will be the same. This property of vectors is the key to the strategy used in the determination of the answer to the above example problem. To further illustrate the strategy, lets consider the vector addition situation described in Example 2 below. Starting at the door of their physics classroom, they walk 2.0 meters, south. They make a right hand turn and walk 16.0 meters, west. They turn right again and walk 24.0 meters, north. ![]() What is the magnitude of their overall displacement. The resultant vector (drawn in black and labeled R ) in the vector addition diagram above is not the hypotenuse of any immediately obvious right trangle.
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