Vector components from initial and terminal points | Vectors | Precalculus | Khan Academy | Summary and Q&A

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March 8, 2015
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Khan Academy
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Vector components from initial and terminal points | Vectors | Precalculus | Khan Academy

TL;DR

Learn how to find the x and y components of a vector using the coordinates of its initial and terminal points.

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Questions & Answers

Q: How can we find the x and y components of a vector based on its initial and terminal points?

To find the x component, subtract the initial x coordinate from the terminal x coordinate. Similarly, for the y component, subtract the initial y coordinate from the terminal y coordinate. In this case, the x component is 15 and the y component is -9.

Q: What are the different notations used to represent vectors?

There are several notations, including unit vector notation (using i and j), column vector notation (placing the components in a column), and numerical representation (directly stating the components). All these notations convey the same vector.

Q: Can vectors be placed in different locations in a coordinate plane?

Yes, vectors can be shifted around in a coordinate plane without changing their magnitude or direction. The important aspect is that the x and y components remain the same.

Q: How is the x component of a vector represented graphically?

The x component of a vector is shown as a vector that is 15 times longer than the unit vector in the horizontal direction. It extends from the initial point to the terminal point along the x-axis.

Summary & Key Takeaways

  • The video explains how to determine the x and y components of a vector based on the coordinates of its initial and terminal points in a coordinate plane.

  • The x component is calculated by finding the change in x between the initial and terminal points, while the y component is found by determining the change in y.

  • Different notations can be used to represent vectors, including unit vector notation, column vector notation, and numerical representation.

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