Video: Finding the Component of a Vector Joining Two Points

Find the components of the vector 𝐴𝐡, where 𝐴 = (βˆ’4.5, 1.2) and 𝐡 = (βˆ’4.5, 5.7).

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Video Transcript

Find the components of the vector 𝐴𝐡, where 𝐴 is the point negative 4.5, 1.2 and 𝐡 is the point negative 4.5, 5.7.

The components of a vector with initial point π‘₯ one, 𝑦 one and terminal point π‘₯ two, 𝑦 two are π‘₯ two minus π‘₯ one, 𝑦 two minus 𝑦 one. This makes sense because to get from π‘₯ one, 𝑦 one to π‘₯ two, 𝑦 two, you have to move π‘₯ two minus π‘₯ one units to the right and then 𝑦 two minus 𝑦 one units up.

In our question, the initial point is 𝐴 with coordinates negative 4.5, 1.2 and our terminal point is 𝐡 with coordinates negative 4.5, 5.7. And comparing with the situation, our diagram, we can just read off the values of π‘₯ one, 𝑦 one, π‘₯ two and 𝑦 two and substitute them into the formula we have for the components of the vector: π‘₯ two minus π‘₯ one, 𝑦 two minus 𝑦 one.

Substituting those values in, we get negative 4.5 minus negative 4.5, 5.7 minus 1.2. And simplifying each component, we get zero, 4.5. So the components of the vector 𝐴𝐡, where 𝐴 is the point negative 4.5, 1.2 and 𝐡 is the point negative 4.5, 5.7, are zero, 4.5.

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