Video: Finding the Components of 3D Vector Which is Represented Graphically

Find the vector 𝐀𝐆 using the graph.

02:00

Video Transcript

Find the vector 𝐀𝐆 using the graph.

One way of answering this question would be to recall that we can find the vector 𝐀𝐁 by subtracting vector 𝐀 from vector 𝐁. This means that in our question, we need to subtract vector 𝐀 from vector 𝐆. Vector 𝐀 is the displacement of point 𝐴 from the origin. This has an 𝑥-component of one, a 𝑦-component of one, and a 𝑧-component of zero. This means that vector 𝐀 is equal to one, one, zero. Vector 𝐆 has an 𝑥-component of four, a 𝑦-component of four, and a 𝑧-component of three. This means that vector 𝐆 is equal to four, four, three.

To calculate vector 𝐀𝐆, we need to subtract one, one, zero from four, four, three. When subtracting vectors, we subtract each component separately. Four minus one is equal to three. When subtracting the 𝑦-components, we also get three. The same is true of the 𝑧-components as three minus zero is equal to three. Vector 𝐀𝐆 is, therefore, equal to three, three, three.

An alternative method here would be to recognize that we have a cube of side length three. Vertices 𝐴 and 𝐺 are opposite corners of the cube. This means that we need to move three units in the 𝑥-, 𝑦-, and 𝑧-direction to get from point 𝐴 to point 𝐺. This confirms that vector 𝐀𝐆 is equal to three, three, three.

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