Question Video: Expressing a Vector in Terms of Unit Vectors Mathematics

Given that 𝐀 = 〈−3, −5〉, express the vector 𝐀 in terms of the unit vectors 𝐢 and 𝐣.

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Video Transcript

Given that vector 𝐀 is equal to negative three, negative five, express the vector 𝐀 in terms of the unit vectors 𝐢 and 𝐣.

When dealing with vectors in two dimensions, we recall that the unit vectors 𝐢 and 𝐣 are vectors of length one in the directions 𝑜𝑥 and 𝑜𝑦, respectively. This means that if point 𝑃 has coordinates 𝑥, 𝑦, then vector 𝐏 is equal to 𝑥𝐢 plus 𝑦𝐣. In this question, we are told that vector 𝐀 is equal to negative three, negative five. This means that 𝑥 is equal to negative three and 𝑦 is equal to negative five. Vector 𝐀 written in terms of its unit vectors 𝐢 and 𝐣 is equal to negative three 𝐢 minus five 𝐣.

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