Homework Help: Calculate Magnitude of Moment in 3D

1. The problem statement, all variables and given/known data

The turnbuckle is tightened until the tension in cable AB is 1.5 kN. Calculate the magnitude of the moment about point O of the force acting on point A.


2. Relevant equations
ƩM_O = sqrt(M_x² + M_y² + M²)


3. The attempt at a solution

First I identified the coordinates of points A and B:

A = (1.6, 0, 2.4)
B = (2.3, 1.4, 0)

OA = r = <1.6, 1.4, 0>
AB = <0.7, 1.4, -2.4>

|AB| = 2.865

λ_AB = AB/|AB|
λ_AB = 0,2443i + 0.4877j - 0.8377k

Then I took the dot product with the tension in the cable AB and the unit vector of AB

T_AB.λ_AB = 0.36645i + 0.73305J - 1.25655K

ƩM_O = rXT_AB

(0-1.75932)i -(-2.81796)J + (1.17288)k

ƩM_O = 3.523

But it says my answer is wrong and I don't know where I'm going wrong.

Suggestions would be appreciated

 

I've just checked my working and found that I miscalculated the dot product.

<1.6, 0, 2.4> X <0.36645, 0.73305, -1.25655>

= -1.75932i + 2.88996J + 1.17288K

When I take the magnitude of this I get 3.58 which is the correct answer.