Vector, centroid of triangle

burgerandcheese

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What do they mean by "point of trisection on the median AD closer to D"? Where is that? I know that vector d is vector AD, but what does vector a represent?
By the way, please tell me how to write vectors on a computer without coding. Should I have to bold the letters like b or is there a way to write vector b with the squiggly line? maybe b_~? Haha
Thanks in advance
 

tkhunny

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What do they mean by "point of trisection on the median AD closer to D"? Where is that? I know that vector d is vector AD, but what does vector a represent?
It means only that length(DG) is length(DA)/3 and that the same relationship holds for the other two medians. I'm not a fan of the terminology, since there are two points on each median that could be called the "point of trisection". Perhaps "a point of trisection" would be better.
 

Dr.Peterson

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View attachment 12244

What do they mean by "point of trisection on the median AD closer to D"? Where is that? I know that vector d is vector AD, but what does vector a represent?
By the way, please tell me how to write vectors on a computer without coding. Should I have to bold the letters like b or is there a way to write vector b with the squiggly line? maybe b_~? Haha
Thanks in advance
I believe they are using a, b, c, and d to mean the position vectors of points A, B, C, and D. So d is not AD, unless A is the origin. Didn't they state what the vectors are?

There are two "points of trisection" on AD, namely the points that divide it into three equal parts. G is the one that is closer to D, so that DG = 1/3 DA, and AG = 2 GD.

Bold works fine.
 

Dr.Peterson

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If it was not explicitly stated in connection with this problem, they may have a convention in general that the position vector of a point is named with the corresponding lower-case letter.
 
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