Video: Expressing a Vector in Cartesian Coordinates

Given that 𝐀 = βˆ’2𝐒 + 4𝐣, write the vector 𝐀 in Cartesian coordinates.

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Video Transcript

Given that vector 𝐀 is equal to negative two 𝐒 plus four 𝐣, write the vector 𝐀 in Cartesian coordinates.

When dealing with vectors in two dimensions, we recall that vectors 𝐒 and 𝐣 are unit vectors in the directions π‘œπ‘₯ and π‘œπ‘¦, respectively. This means that any vector 𝐏 with Cartesian coordinates π‘₯𝑦 can be written π‘₯𝐒 plus 𝑦𝐣. In this question, we’re told that vector 𝐀 is equal to negative two 𝐒 plus four 𝐣. This means that our π‘₯-value is negative two and our 𝑦-value is four. Vector 𝐀 written in Cartesian coordinates is equal to negative two, four.

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