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Question Video: Expressing a Vector in Cartesian Coordinates Mathematics • 12th Grade

Given that 𝚨 = 5𝐒 βˆ’ 7𝐣, write vector 𝚨 in Cartesian coordinates.

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Video Transcript

Given that vector 𝚨 is equal to five 𝐒 minus seven 𝐣, write vector 𝚨 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‘¦. If we are given any point 𝑃 with coordinates π‘₯𝑦, then vector 𝐏 is equal to π‘₯𝐒 plus 𝑦𝐣. In this question, we are told that vector 𝚨 is equal to five 𝐒 minus seven 𝐣. This means that π‘₯ is equal to five and 𝑦 is equal to negative seven. Vector 𝚨 written in Cartesian coordinates is equal to five, negative seven.

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