Question

AFTER Cartesian vector form?
Crate = 140-lb

0 = (-6/7)T_AB - (6/7)T_AC
0 = (3/7)T_AB - (2/7)T_AC
0 = (2/7)T_AB + (3/7)T_AC - 140
?

Answer 1

you can put the origin anywhere you like, but A looks like a good place

Answer 2

so

0 = (-6/7)T_AB - (6/7)T_AC
0 = (3/7)T_AB - (2/7)T_AC
0 = (2/7)T_AB + (3/7)T_AC - 140 (weight not described in posted pic)

?

Answer 3

@satellite73 @Directrix @Loser66

Answer 4

Your 2nd and 3rd equations are ok.
but the forces in the first are balanced by AD
in other words, the equation should read
0 = (-6/7)T_AB - (6/7)T_AC + T_AD

you can use eq 2 and eq 3 to solve for T_AB and T_AC
and then use those values in the 1st equation to find T_AD

Answer 5

What? There is no T_AD with a length.

Answer 6

T_AD is the tension in the direction A to D.
all of these vectors are unit length, and then scaled by the tension.

Answer 7

I thought I could ignore it

Answer 8

AD is part of the system.