Proving a 2:1 ratio triangle having a Zero Vector

In summary, the individual equations GP = GQ + QP, GQ = GP + PQ, and GR = GP + PR are provided to solve for the equations GP + GQ + GR = GQ + 2GP + PR. The 2:1 ratio fact should be incorporated and the mid points of each side should be named as A, B, and C to use in the equations GA, GB, and GC.
  • #1
aeromat
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Homework Statement


I need help once again with this question below:
62-17-p292.png


Thanks,
aeromat



The Attempt at a Solution



This is what I have so far:
GP = GQ + QP
GQ = GP + PQ
GR = GP + PR

GP + GQ + GR = GQ + QP[-] + PQ[+] + GP + PR + GP
GP + GQ + GR = GQ + 2GP + PR

I am stuck now. I took the approach of taking GP + GQ + GR individually and finding their vector components.
 
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  • #2
you haven't used the 2:1 ratio fact anywhere. try using that.

hint: name the mid points of each side A,B,C. And try to use GA, GB, GC in your equations.
 

FAQ: Proving a 2:1 ratio triangle having a Zero Vector

What is a 2:1 ratio triangle?

A 2:1 ratio triangle is a triangle where the ratio of the lengths of two sides is 2:1. This means that one side is twice as long as the other side.

How can you prove that a triangle has a 2:1 ratio?

To prove that a triangle has a 2:1 ratio, you can use the Pythagorean theorem. First, measure the lengths of the two sides in question. Then, square each length and add them together. If the sum of the squares is equal to the square of the third side, then the triangle has a 2:1 ratio.

What is a Zero Vector in relation to a 2:1 ratio triangle?

A Zero Vector is a vector with a magnitude of zero. In the context of a 2:1 ratio triangle, a Zero Vector would refer to a side with a length of zero.

How can you prove that a 2:1 ratio triangle has a Zero Vector?

To prove that a 2:1 ratio triangle has a Zero Vector, you can use the Pythagorean theorem. If one of the sides has a length of zero, then the sum of the squares of the other two sides will also equal zero. This is because any number squared will equal zero if the number itself is zero.

Why is it important to prove a 2:1 ratio triangle has a Zero Vector?

Proving that a 2:1 ratio triangle has a Zero Vector can help to verify the accuracy of measurements and calculations. It can also be used to identify any errors in the data or measurement process. Additionally, understanding the relationship between a 2:1 ratio triangle and a Zero Vector can be useful in various applications, such as engineering and physics.

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