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# Splitting a Vector into two

A vector has an effect in any direction except the one at right angles to it. Sometimes a vector has two independent effects which need to be isolated. Just as the combined effect of two vectors acting on a single object can be calculated, two separate effects of a single vector can be found by splitting the vector into two components. Provided that the directions of the two **components** are chosen to be at right angles, each one has no effect in the direction of the other so they are

considered to act independently.

The process of splitting a vector into two components is known as **resolving** or **resolution of** the vector.

The diagram shows the tension (T) in a cable holding a radio mast in place. The force is pulling the mast both vertically downwards and horizontally to the left.

To find the effect of the tension in these directions, **T** can be split into two components, shown as **T _{H }**(the horizontal component) and

**T**(the vertical component) in the diagram. You should check that according to the rules of vector addition,

_{V}**T**.

_{H}+ T_{V}= TTo find the magnitude of **T _{H}** and

**T**the following rules apply:

_{V}the component of a vector **a** at an angle θ to its own angle is acosθ

the component of a vector **a** at an angle (90° – θ) to its own angle is asinθ

The application of these rules is shown in the right-hand diagram above.

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