Question

Moment of force and a masthead

Answer 1

I'll show my work in a picture following this one. I know its messy looking, but I just want to know if I got the right answer T.

Answer 2

Here's my answer.

Answer 3

hint:
we have to solve this vector equation:
\[{\mathbf{O}}{{\mathbf{P}}_{\mathbf{1}}}{\mathbf{ \times F + O}}{{\mathbf{P}}_{\mathbf{2}}}{\mathbf{ \times T = 0}}\]

Answer 4

where P_! is the point at which the force whose modulus is 5kN is applied, and P_2 is the point at which, the force, whose modulus is T, is applied.
next step is:

Answer 5

\[\left\| {\begin{array}{*{20}{c}}
{{\mathbf{\hat x}}}&{{\mathbf{\hat y}}}&{{\mathbf{\hat z}}} \\
{ - 90}&0&{60} \\
{5\cos \left( {240} \right)}&0&{5\cos \left( {150} \right)}
\end{array}} \right\| + \left\| {\begin{array}{*{20}{c}}
{{\mathbf{\hat x}}}&{{\mathbf{\hat y}}}&{{\mathbf{\hat z}}} \\
{120}&0&{60} \\
{T\frac{2}{{\sqrt {29} }}}&0&{ - T\frac{5}{{\sqrt {29} }}}
\end{array}} \right\| = {\mathbf{0}}\]