Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 317

What do vectors in a triangle represent?

A vector in the form of a line segment has magnitude (the length of the line segment) and direction (going from its tail to its head). We can represent this using a column vector, i.e, brackets, inside of which there is, e.g, a 3 on top of another 3, indicating that the line goes in the north east direction (the tail starting at point x, the head located at a point 3 to the right, 3 up).

But what about vectors in shapes - triangles in the case of my introduction, courtesy of Maths Genie?

The line segments (the sides of the triangles) are represented by values such as 2a, b, -2a+b, etc; not by pairs of co-ordinates as with the 3,3 above.

What do these values mean?

They can’t mean the length of the line segment (the side of the triangle) given that sometimes they are negative. Also, the value from, for example, A to B is the negative of B to A, and the length of the side can’t have two values.

Maths Genie doesn’t explain what 2a, b, etc means.

I looked elsewhere but didn't find a simple explanation.

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: What do vectors in a triangle represent?

hi

a and b are vectors.  They could be any vectors. I've just chosen a couple of random ones.  2a + b means go along a twice and then b once.  I've shown the resultant vector in green.

Note that I've started them anywhere on the diagram, since the magnitude and direction is the same wherever you start from.  When adding them I've started the second vector from where the first left off.

If they were vectors to show movement then you can see where you'd end up if you did 2a + b as a journey.  They could also be forces in which case 2a + b shows the result of combining the forces.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 317

Re: What do vectors in a triangle represent?

Ah, thanks, Bob.

So a=2,1
and b  =1,-3
and 2a+b= 5,-1

?

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: What do vectors in a triangle represent?

Yes, for my random choice for a and b.  You can try it with your own choices.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob