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The graphic diagram below shows there are infinite solutions (non-unique) to this problem.

Steps:

1. Draw the gravity load to scale and mark the ends "a" and "b".

2. Draw a construction line parallel to the vector $T_1$ from point "a".

3. Draw a construction line parallel to the vector $T_3$ from point "b".

4. Now make a line parallel to the vector $T_2$, but, what is the unique line length required to close the vector loop???

The graphic diagram below shows there are infinite solutions (non-unique) to this problem.

Steps:

1. Draw the gravity load to scale and mark the ends "a" and "b".

2. Draw a construction line parallel to the vector $T_1$ from point "a".

3. Draw a construction line parallel to the vector $T_3$ from point "b".

4. Now make a line parallel to the vector $T_2$, but, what is the unique line length required to close the vector loop???

Let's try another sequence to draw the vector loop.

1. Draw a line (3-3) parallel to $T_3$.

2. Draw a line (1-1) parallel to $T_1$ and let it intercept the line 1-1.

3. Set the scaled vector 6.21 on line 3-3 at 2 locations, and call the upper points "a" and "b" respectively.

4. Draw two lines parallel to $T_2$ and let the lines pass the points "a" and "b", now we get two sets of solutions, which can be more.

To solve for the 3 unknowns, you need 3 equations.

There are 2 static equilibrium equations readily available - $\sum Fx = 0, \sum Fy = 0$. The last equation is formed by applying the "Cosine Laws" to the triangle bounded by $T_1, T_2$ and $T^*$ (see sketch below).

The graphic diagram below shows there are infinite solutions (non-unique) to this problem.

Steps:

1. Draw the gravity load to scale and mark the ends "a" and "b".

2. Draw a construction line parallel to the vector $T_1$ from point "a".

3. Draw a construction line parallel to the vector $T_3$ from point "b".

4. Now make a line parallel to the vector $T_2$, but, what is the unique line length required to close the vector loop???

To solve for the 3 unknowns, you need 3 equations.

There are 2 static equilibrium equations readily available - $\sum Fx = 0, \sum Fy = 0$. The last equation is formed by applying the "Cosine Laws" to the triangle bounded by $T_1, T_2$ and $T^*$ (see sketch below).

To solve for the 3 unknowns, you need 3 equations.

There are 2 static equilibrium equations readily available - $\sum Fx = 0, \sum Fy = 0$. The last equation is formed by applying the "Cosine Laws" to the triangle bounded by $T_1, T_2$ and $T^*$ (see sketch below).