Question Video: Expressing a Vector in Component Form Physics

Write 𝐀 in component form.

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Video Transcript

Write 𝐀 in component form.

The diagram shows vector 𝐀 to be drawn onto a grid. We are asked to write vector 𝐀 in component form. The component form of a vector is typically written as π‘Ž sub π‘₯ 𝐒 plus π‘Ž sub 𝑦 𝐣, where π‘Ž sub π‘₯ is the magnitude of the π‘₯-component of the vector and π‘Ž sub 𝑦 is the magnitude of the 𝑦-component of the vector. 𝐒 and 𝐣 represent unit vectors, with 𝐒 being in the direction of the horizontal axis and 𝐣 being in the direction of the vertical axis. Because we’re handwriting our answers, we use a half arrow over the letter 𝐀 to represent that it’s a vector. In text form, we bolded it. In the 𝐒 and 𝐣, we see little hats to represent that they’re unit vectors. In text form, these can also be bolded.

To find the component form of vector 𝐀, we need to determine how much of vector 𝐀 is in the horizontal direction and how much of vector 𝐀 is in the vertical direction. Looking at the grid, we can see that vector 𝐀 is one, two, three units to the left of our screen. This is considered negative three. We could then say that the 𝐒-component of our vector has a magnitude of negative three. Looking back at the grid, we can see that the 𝑦-component or the vertical direction has a magnitude of one, two units pointing towards the top of the screen, which would be a positive two. We could, therefore, say that the 𝐣-component of our vector has a magnitude of two. Based on the diagram, the component form of vector 𝐀 is equal to negative three 𝐒 plus two 𝐣.

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