Find the Tensions in the Cables

[Northbysouth]

Homework Statement

Determine the tensions in cables AB, AC, and AD.

Homework Equations

The Attempt at a Solution

I mad point A (0,0,0)
B = (2.6, -4.2, 4.4)
C = (-2.6, -1.6, 4.4)
D = (0, 2.5, 4.4)
Firstly I found the unit vectos of AB, AC and AD, which are as follows

$\hat{}n$_AB = <2.6, - 4.2, 4.4>/ 6.615134

$\hat{}n$_AB = <0.393041i - 0.634908j + 0.665141k

$\hat{}n$_AC = <-2.6, -1.6, 4.4>/5.35537

$\hat{}n$_AC = <-0.48549i -0.29876j +0.821605k>

$\hat{}n$_AD = <0i +2.5j + 4.4k>/5.06063
$\hat{}n$_AD = oi + 0.494009j + 0.86945k

Then I took each unit vector and multiplied it by the force, 113 lb

T_AB = T_AB$\hat{}n$<sub>AB[/SUB = TAB(0.39394i - 0.634908j + 0.665141k)

TAC = TAC$\hat{}n$AC = TAC(-0.48549i -0.29876j + 0.821605k)

TAD = TAD$\hat{}n$AD =TAD(0i + 0.494009j +0.86956k)

i: 0.39304*TAB - 0.48549T^AC + 0TAD

j: -0.634908TAB - 0.29876TAC + 0.494009TAD

k: 0.665141TAB + 0.821605TAC + 0.86945TAD

I then put this into a matrix and then used my calculator to solve for TAB, TAC and TAD

I got:

TAB = 39.3261
TAC = 31.9374
TAD = 69.7967

But it says my answer is wrong and I don't know where I'm going wrong. Help would be appreciated</sub>

 

[Northbysouth]

Just found my mistake. I defined the location of B incorrectly. B = (2.6, -1.6, 4.4). Using these values I get

TAB = 41.9316
TAC = 41.9316
TAD = 50.7184