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Problem 2 Easy Difficulty

What is the relationship between the point $ (4, 7) $ and the vector $ \langle 4, 7 \rangle $? Illustrate with a sketch.

Answer

On the coordinate plane, the point $(4,7)$ is a location whereas the vector $\langle 4,7\rangle$ is a directed arrow from a point $\left(x_{1}, y_{1}\right)$ to another point $\left(x_{2}, y_{2}\right)$ whenever $x_{2}-x_{1}=4$ and $y_{2}-y_{1}=7 .$ The point $(4,7)$ is unique on the coordinate plane, but the vector $\langle 4,7\rangle$ is not so long as it satisfies the condition mentioned above. Only when the vector $\langle 4,7\rangle$ initiates from the origin, then the point $(4,7)$ is the terminal point (i.e., the tip of the arrow) of the vector.

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Video Transcript

So we probably want to find the relationship Between the .47 and the Vector 4 7. So for example, we look at the .47 And vector for seven. Um We know that we could have the base right here at the origin and we could draw an arrow Up to here and this would be the Vector 4 7. So that's definitely a similarity they have. However, differences, we could move this vector over here over here, it could be the vector for seven, but it can be moved all over the place now and it would still be the vector for seven, even though it's not at that actual point. So that would be the main difference. But the relationship that they have is that if we let the initial coordinate Be the origin, then the .47 is the terminating point or the tail of the given vector.