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Vectors, Velocity Vectors, Components of Vectors

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More Lessons for High School Physics
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A series of free Online High School Physics Video Lessons.

In this lesson, we will learn

  • how to find the magnitude and direction of a vector
  • to understand the difference between vector and scalar quantities
  • how to express velocity as a vector
  • how to find the components of a vector

Vector Direction

A vector contains two types of information: a magnitude and a direction. The magnitude is the length of the vector while the direction tells us which way the vector points. Vector direction can be given in various forms, but is most commonly denoted in degrees. Acceleration and velocity are examples of vectors.
In these video, we find the magnitude (length) of some vectors and find the angle associated with them.

Magnitude and Direction of a Vector,
Example 1. <−3, 4>
Magnitude and Direction of a Vector,
Example 2. <−2, −5> Magnitude and Direction of a Vector,
Example 3. <2, 6> , <3, −10>

Vector and Scalar Quantities

A scalar quantity contains a magnitude and operates independently of direction while a vector quantity contains a direction. Most scientific data are scalar. A few examples of scalar quantities include time, mass and speed. Examples of vector quantities include velocity and displacement.
Understanding the differences between vectors and scalar quantities

Velocity Vectors

A velocity vector represents the rate of change of the position of an object. The magnitude of a velocity vector gives the speed of an object while the vector direction gives its direction. Velocity vectors can be added or subtracted according to the principles of vector addition.
This video shows how to solve a velocity vector problem.

Components of Vectors

Two-dimensional vectors have two components: an x vector and a y vector. Each of these vector components is a vector in the direction of one axis. The sum of the components of vectors is the original vector. Three-dimensional vectors have a z component as well. Understanding the components of vectors.
In this video, we are given the magnitude and direction angle for the vector and want to express the vector in component form.
Finding the Components of a Vector,
Ex 1
What are the x and y components of a vector with a magnitude of 8 and at an angle of 60 degrees from the origin? Finding the Components of a Vector,
Ex 2 - Express the given vectors in component form.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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