If a charged particle of charge q� is travelling with a velocity v� in a magnetic field B,�,  then the force that that charged particle feels is given by F=qv×B.�=��×�.  In this case, the force F� is also a vector quantity, since it has both a magnitude and a direction. So the cross product plays an important role in physics and engineering.   Now suppose that a proton with some positive charge q� is traveling in the xy��-plane with a velocity in the direction of the vector v=⎛⎝⎜3−20⎞⎠⎟�=(3−20)  and that the magnetic field B�  is a uniform field pointing straight up in the z� direction, perpendicular to the xy��-plane. Then the direction of the force that the moving proton feels is in the direction

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 13CR
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If a charged particle of charge q� is travelling with a velocity v� in a magnetic field B,�,  then the force that that charged particle feels is given by

F=qv×B.�=��×�. 

In this case, the force F� is also a vector quantity, since it has both a magnitude and a direction. So the cross product plays an important role in physics and engineering.

 

Now suppose that a proton with some positive charge q� is traveling in the xy��-plane with a velocity in the direction of the vector v=⎛⎝⎜3−20⎞⎠⎟�=(3−20)  and that the magnetic field B�  is a uniform field pointing straight up in the z� direction, perpendicular to the xy��-plane. Then the direction of the force that the moving proton feels is in the direction

 

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