$2\mathrm{.}1$ A light horizontal beam is $15$ m long and is supported at the left end and $3$ m from the right end.

The beam carries the following point loads:

$120$ N two metres from the left$-$hand end

$80$ N five metres from the left$-$hand end

$90$ N at the right$-$hand end

$2\mathrm{.}1\mathrm{.}1$ Make a neat line sketch of the beam and clearly show all its dimensions and loads.

$2\mathrm{.}1\mathrm{.}2$ Calculate the reactions of both points of support by taking moments about both supports. $($Ignore the weight of the beam.$)$

$2\mathrm{.}1\mathrm{.}3$ Check the answer by balancing upward and downward forces.