Any vector can be replaced by two vectors which, acting together, exactly duplicate the effect of the original vector. These replacement vectors are called the * components of the vector*, and are usually chosen perpendicular (at right angles) to each other. Another name for these perpendicular component vectors is

**rectangular components**. The process of of breaking a 2D vector into its vertical (y) and horizontal (x) components is known as

*resolving a vector*. The first video shows how a vector in the first quadrant is broken down into its rectangular components.

Another way to represent the answer in the video is by writing it in **rectangular form**:

**v** = a**i** + b**j** where a = v_{x} and b = v_{y}

âˆ´ **v** = 25.3**i** + 49.3**i**

Note that **i** is horizontal component vector of the vector **v**, and **j** is vertical component vector. The vector sum a**i** + b**j** is called a **linear combination** of the vector **i** and **j**. The magnitude of v = a**i** + b**j** is given by:

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The process above can also be reversed, where the rectangular components are added up to obtain the **resultant vector**. This is typically done using the tangent ratio and the Pythagorean theorem. The technique is shown below:

Challenge Question:Find the resultant of two

perpendicular vectorswhose magnitudes are 485 and 627. Also find the angle that it makes with the 627-magnitude vector.

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