Video: The Components of a Vector

Find the components of the vector ๐ด๐ต, where ๐ด = (5, 2) and ๐ต = (17, 23).

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Video Transcript

Find the components of the vector ๐ด๐ต, where ๐ด is the point with coordinates five, two and ๐ต is the point with coordinates 17, 23.

So weโ€™ve been given the initial and terminal points of a vector and asked to find its components. To do this, we need to record that if a vector has an initial point with coordinates ๐‘ฅ one, ๐‘ฆ one and a terminal point with coordinates ๐‘ฅ two, ๐‘ฆ two, then the components of the vector can be found by subtracting the coordinates of the initial point from the terminal point.

The components of the vector are ๐‘ฅ two minus ๐‘ฅ one, ๐‘ฆ two minus ๐‘ฆ one. So letโ€™s apply this to the vector ๐ด๐ต. The first component of the vector ๐ด๐ต, the horizontal component, is 17 minus five.

The second component the vertical part is 23 minus two. Therefore, in component form, the vector ๐ด๐ต is 12, 21.

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