[1.7 | 11 | 24] A treasure map has n villages marked on it, and it contains the following instructions: Start at village A, go 1/2 of the way to B, 1/3 of the way to village C, 1/4 of the way to village D, and so forth. The treasure is buried at the last stop. Problem: You lose the instructions, and don't know in what order to select the villages. Show that it doesn't matter! You can still find the treasure.
The solution is in the title.
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Reference:
[1]
Monday, March 31, 2008
Saturday, March 15, 2008
What's the point?
If the vector
represents the segment AB, and the midpoint of AB is (2,1), find A and B.
This is one of the problems which is easier solved by utilizing the properties of vectors.
The other solution is the conventional distance formula to solve for the coordinates of A and B but this actually takes longer because there are four unknowns in this case. At least two simultaneous equations may be required.
On the other hand, the vector method hinges on the vector property that its components represent the difference between the coordinates at endpoints. With this, the coordinates of A and B can be solved using a simple linear equation, one unknown at a time.
...
...
Reference:
[1]
represents the segment AB, and the midpoint of AB is (2,1), find A and B.This is one of the problems which is easier solved by utilizing the properties of vectors.
The other solution is the conventional distance formula to solve for the coordinates of A and B but this actually takes longer because there are four unknowns in this case. At least two simultaneous equations may be required.
On the other hand, the vector method hinges on the vector property that its components represent the difference between the coordinates at endpoints. With this, the coordinates of A and B can be solved using a simple linear equation, one unknown at a time.
...
...
Reference:
[1]
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