Question Video: Expressing a Given Vector in Terms of Fundamental Unit Vectors

Given that 𝐀 = ⟨0, 0, 10⟩, express vector 𝐀 in terms of the unit vectors 𝐢, 𝐣, and 𝐤.

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Video Transcript

Given that vector 𝐀 is equal to zero, zero, 10, express vector 𝐀 in terms of the unit vectors 𝐢 hat, 𝐣 hat, and 𝐤 hat.

We recall that the unit vectors 𝐢, 𝐣, and 𝐤 can be shown on the three-dimensional coordinate plane as follows. The unit vector 𝐢 hat corresponds to one unit in the 𝑥-direction. The unit vector 𝐣 hat corresponds to one unit in the 𝑦-direction. And the unit vector 𝐤 hat represents one unit in the 𝑧-direction. In this question, we are told that vector 𝐀 is equal to zero, zero, 10. This means that the 𝑥-component is equal to zero, the 𝑦-component is equal to zero, and the 𝑧-component is equal to 10. Vector 𝐀 is therefore equal to zero 𝐢 plus zero 𝐣 plus 10𝐤. This simplifies to 10𝐤. In terms of the unit vectors 𝐢, 𝐣, and 𝐤, vector 𝐀 is equal to 10𝐤.

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