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.