Question Video: Expressing a Vector in Terms of Unit Vectors Mathematics • 12th Grade

Given that 𝐀 = ⟨0, 2⟩, express the vector 𝐀 in terms of the unit vectors 𝐒 and 𝐣.

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Video Transcript

Given that vector 𝐀 is equal to zero, two, express the vector 𝐀 in terms of the unit vectors 𝐒 and 𝐣.

When dealing with vectors in two dimensions, we know that the unit vectors 𝐒 and 𝐣 are vectors of length one in the directions π‘œπ‘₯ and π‘œπ‘¦, respectively. This means that given any point 𝑃 with coordinates π‘₯, 𝑦, vector 𝐏 is equal to π‘₯𝐒 plus 𝑦𝐣. In this question, we are told that vector 𝐀 is equal to zero, two. This means that π‘₯ is equal to zero and 𝑦 is equal to two. As π‘₯ is equal to zero, we can simply write vector 𝐀 as two 𝐣.

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