Question Video: The Components of a Vector on a Grid

The components of the vector 𝐮 are ⟨−1, −2⟩ as the terminal point of the vector is −1 units right (1 unit left) of the initial point and −2 units up (2 units down) from the initial point. What are the components of the vector 𝐯?

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Video Transcript

The components of the vector 𝐮 are negative one, negative two as the terminal point of the vector is negative one units right or one unit left of the initial point and negative two units up or two units down from the initial point. What are the components of the vector 𝐯?

We know that any vector in two dimensions has an 𝑥- and 𝑦-component. These are the number of units we need to move from the initial point of the vector to the terminal point. The 𝑥-component is positive if we move to the right and negative if we move to the left. Likewise, the 𝑦-component is positive if we move upwards and negative if we move downwards.

This means that the vector 𝐮 has components negative one and negative two as we move one unit left and two units down. The vector 𝐯 moves three units to the left, which means that the 𝑥-component is equal to negative three. Vector 𝐯 also moves four units down, so the 𝑦-component is equal to negative four.

Vector 𝐯 is therefore equal to negative three, negative four.

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