Use vectors to find coordinate of a point

In summary, the problem presents a right triangle with coordinates for points B and C, and asks for the coordinates of point A. The attempted solution involved using the dot product and the magnitude of vectors, but the calculations became messy. The poster eventually realized their mistake and found the solution.
  • #1
mesa
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Homework Statement



So for this problem we are shown a right triangle with point B at (2,1), C at (7,0) and A(x,y). 'A' also happens to rest at the right angle of our triangle. What is the coordinate of 'A'

The Attempt at a Solution



I tried this one a couple ways. For example the dot product of AB and AC will be zero but that gets messy. I then tried using the magnitude of each vector and used Pythagoras but it gets messy that way too. I am sure it is something simple but it's been a long night...
 
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  • #2
It probably is. Right triangles are tricky that way. However, you have shown no work, and it is difficult to see where you went so horribly wrong.
 
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  • #3
SteamKing said:
It probably is. Right triangles are tricky that way. However, you have shown no work, and it is difficult to see where you went so horribly wrong.

Sorry, I thought my method was at issue... It is funny how sometimes when re-writing on a keyboard a problem can fix itself. My ^2 terms canceled so I am good to go, it pays to follow protocol :)
 
  • #4
Not that I am bothered by it, I simply want to know why this thread was 'moved'?
 

FAQ: Use vectors to find coordinate of a point

What is a vector and how is it used to find the coordinate of a point?

A vector is a mathematical quantity that has both magnitude (size) and direction. It is commonly represented by an arrow pointing in the direction of the vector. To find the coordinate of a point using a vector, we use the vector's magnitude and direction to determine the distance and direction from the origin to the point.

How do I represent a vector?

A vector can be represented in several ways, but the most common ways are using Cartesian coordinates (x and y values) or using an ordered pair (x,y). For example, a vector with a magnitude of 5 and a direction of 30 degrees can be represented as (5*cos(30), 5*sin(30)) or (4.33, 2.5).

Can I use any vector to find the coordinate of a point?

Yes, as long as the vector has a known magnitude and direction, it can be used to find the coordinate of a point. However, it is important to make sure that the vector is aligned with the correct coordinate system.

What is the difference between a position vector and a displacement vector?

A position vector is a vector that represents the location of a point in relation to a fixed origin. It is typically denoted by the letter "r". On the other hand, a displacement vector is a vector that represents the change in position of a point from its initial position to its final position. It is typically denoted by the letter "d".

Can vectors be used in three-dimensional space?

Yes, vectors can be used in three-dimensional space just like they are used in two-dimensional space. In three-dimensional space, a vector has three components (x, y, and z) and can be represented using ordered triplets (x,y,z).

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