Rev. Notes > AS > Physical quantities and units Previous Topic Physical quantities and units Next Topic Topics
 Physics Areas of Physics Interdisciplanary areas of physics Quantities in Physics Base Units Convention for indicating units Derived Units S.I. Units (International System of Units) Supplementary units Homogeneity of equations Significant figures Rules of Significant figures Further discussion on Significant figures Dimensions Scientific notation The Avogadro's Constant Scalars and Vectors Addition and subtraction of co-planar vectors Rectangular components of a vector

## Addition and subtraction of co-planar vectors

For Example: 3kg + 4 kg = 7 kg

Adding vectors needs much more care. You have to take into account their magnitude and direction.

For Example: What's 3N + 4N? Well, it depends on the directions! Look at the possibilities...

Note: 1N is not balanced, so if these two forces 3N and 4N will be applied on an object, the object will accelerate with 1N force towards right.

Now consider the given diagram in which 3N force is acting on the object towards right and 4N force is acting on the same object upward. Resultantly the object will move with resultant force of 5N in the direction shown below.

So in other words, you add vectors geometrically (using geometry). You should be able to do this using accurate diagrams (don't forget your protractor) or by using Pythagoras.

Resultant Vectors

The resultant vector is the one that you get when you add two or more vectors together. It is a single vector that has the same effect as all the others put together. Finding the resultant vector when the forces are in different directions can be tricky if you don't like Pythagoras, so here's a couple to get you going!

Worked Example:

Resolving Vectors into Components

We have just shown that any two vectors can be represented by a single resultant vector that has the same effect. You can do the same thing in reverse! Any single vector can be represented by two other vectors (components), which would have the same effect as the original one:

You need to use trigonometry to find the two components of a vector. Remember the two components will always be at right angles. These are called rectangular components of vector.

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