This is very easy, if the given is one mirror (iR=rR) or the incident ray is equal to reflected ray. If the given is two or more, to find the reflected ray you need to know the measure of the angle formed by the two mirrors, the mathematical solution for this is the |Reflected ray of mirror 1 + Reflected ray of mirror 2| = |the measurement of the angle that mirror 1 and 2 form| or when transmuted |m(angle)m1,m2-iRM1|=rRM2 .

For example, there are 3 mirrors. Second mirror is 100 degrees to the left of the First mirror, and the third mirror is 40 degrees to the left of the second mirror. The Incident ray hit mirror 1 at an angle of 40 degrees the reflected angle of mirror is 60 degrees following the given formula (|[m(angle)m1,m2]-iRM1|=rRM2) or (|100-40|=60) so it follows that the Reflected Ray of mirror 3 is 20 degrees using the formula again.

It's very simple and easy, this is the "so called" shortcut. ^_^

First, draw the given displacements starting from the origin, remember that after each line you should always name it's points. Always use a ruler in drawing the displacement. If the given displacements does not lie exactly at the x-axis or y-axis remember to use a protractor to accurately plot the given angle. Minimize the scale by declaring it as a smaller scale, (ex. 1km-1cm). After drawing all the displacements, measure the distance of the resultant and the origin. Multiply the measurement the original scale, and use a protractor to find the magnitude of the resultant vector, do not forget to include its direction either it's from north of east etc.

Start by creating a table with the first column labeled as vector, the second as x-component and the last column as y-component. Draft the right triangle for the given problem. Find the x and y-components using the trigonometric functions(SOHCAHTOA). Find the sum of the x and y-components. The magnitude can be determined by the use of the Pythagorean theorem and the inverse tangent function for the direction.