Quantities with magnitude and direction, such as force and velocity, added tip-to-tail or by components.
A vector has magnitude and direction and adds by components or tip-to-tail. Unit vectors i, j, k give a basis. Position, velocity, force and fields are vectors. The magnitude is ‖v‖=√(vx²+vy²+vz²).
(3,4) has magnitude 5 and direction atan(4/3) ≈ 53°.
Vectors combine magnitude and direction, which is needed for every force, velocity, field and displacement in mechanics and electromagnetism.
Quantities with magnitude and direction, such as force and velocity, added tip-to-tail or by components.
Vectors combine magnitude and direction, which is needed for every force, velocity, field and displacement in mechanics and electromagnetism.
Add components along each axis for the numerical method. Place them tip to tail for the graphical method, and the resultant runs from the first tail to the last tip.
A vector of length one that points in a direction. Dividing a vector by its magnitude gives its unit vector.
Typical applications include summing forces acting on a bracket, computing the resultant wind load on a tower and describing the direction of a magnetic field at a sensor.
Study "Coordinate geometry" first (topic 17 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
Scalar multiplication scales length. Unit vector = v/‖v‖. Components are found with trigonometry.
(3,4) has magnitude 5 and direction atan(4/3) ≈ 53°.
The next topic is "Dot product", which builds directly on this one.
It is classed as Beginner in Engineering Mathematics (topic 18 of 104). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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