Question Video: Identifying Vectors with the Same Direction on a Coordinate Grid Mathematics

Which vector has the same direction as 𝐚?

01:26

Video Transcript

Which vector has the same direction as vector 𝐚?

If two vectors have the same direction on a coordinate plane, then the lines must be parallel. This means that they never meet. So, it is quite obvious from the diagram that the vector that has the same direction as 𝐚 is vector 𝐝. Vectors 𝐚 and 𝐛 have the same initial point. Therefore, they cannot be in the same direction. In a similar way, vectors 𝐚 and 𝐜 have the same terminal point. This means that they cannot be in the same direction. If two line segments have the same initial point or terminal point, they cannot be parallel. Therefore, the vectors cannot be in the same direction.

We can actually go one stage further in this question. We can see from the grid that vector 𝐚 is equal to four, two. From the initial point to the terminal point, we move four units right and two units up. This is also true of vector 𝐝. We can, therefore, conclude that vectors 𝐚 and 𝐝 have the same magnitude as well as the same direction. When two vectors have the same 𝑥- and 𝑦-component, they will have the same magnitude and direction.

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