Question Video: Expressing a Given Vector in Cartesian Coordinates Mathematics

Given that 𝐀 = 2𝐤, write vector 𝐀 in Cartesian coordinates.

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Video Transcript

Given that vector 𝐀 is equal to two 𝐤, write vector 𝐀 in Cartesian coordinates.

We begin by recalling that the fundamental unit vectors 𝐢 hat, 𝐣 hat, and 𝐤 hat can be shown on a three-dimensional coordinate plane as follows. One unit in the 𝑥-direction is denoted 𝐢 hat. In the same way, one unit in the 𝑦-direction is denoted 𝐣 hat. And one unit in the 𝑧-direction is denoted 𝐤 hat.

In this question, vector 𝐀 is equal to two 𝐤. This means that its 𝑥- and 𝑦-components are equal to zero. When writing a vector in terms of its Cartesian coordinates, the 𝑥-component is the displacement in the 𝑥-direction; the 𝑦-component, the displacement in the 𝑦-direction; and the 𝑧-component, the displacement in the 𝑧-direction. As already mentioned, both 𝑥 and 𝑦 are equal to zero.

As vector 𝐀 is equal to two multiplied by the unit vector 𝐤 hat, 𝑧 is equal to two. The vector two 𝐤 written in Cartesian coordinates is zero, zero, two.

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