Video: The Components of a Vector on a Grid

Find the components of vector 𝐯 shown on the grid of unit squares.

01:12

Video Transcript

Find the components of vector 𝐯 shown on the grid of unit squares below.

We know that any vector drawn in two dimensions will have an 𝑥- and 𝑦-component. The 𝑥-component is positive if it is moving to the right and negative if it is moving to the left. The 𝑦-component is positive if the vector is moving upwards and negative if moving downwards. The vector 𝐯 can therefore be written in terms of its components as shown.

Any horizontal vector, as in this case, will have a 𝑦-component equal to zero. Whilst it is not relevant for this question, we also know that any vertical vector will have an 𝑥-component equal to zero. We see from the diagram that vector 𝐯 moves six unit squares to the right. This means that the 𝑥-component of vector 𝐯 is six. We can therefore conclude that vector 𝐯 has components six, zero.

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