1.5.8 Scalars & Vectors

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Scalars & Vectors

• Quantities can be one of two types: A scalar or a vector
• Scalars are quantities that have only a magnitude (a number describing how big they are)
• Vectors have both magnitude and direction

The cars in the above diagram have the same speed (a scalar quantity) but different velocities (a vector quantity)

• Force is a vector quantity – it has both magnitude and direction

The force is represented by the arrow. Its length gives the magnitude (size) of the force and the arrow also shows its direction

• Some common scalars and vectors are given below

• Note: Some vector quantities (such as displacement and velocity) are very similar to some corresponding scalar quantities (distance and speed)

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• Vectors can be added together to produce a resultant vector. The rules for doing this, however, are slightly different to scalars:
• If two vectors point in the same direction, the resultant vector will also have the same directions and its value will be the result of adding the magnitudes of the two original vectors together
• If two vectors point in opposite directions then subtract the magnitude of one of the vectors from the other one. The direction of the resultant will be the same as the larger of the two original vectors

Diagram showing the result of adding two aligned vectors (forces) together

• If the two vectors point in completely different directions, then the value of the resultant vector can be found graphically:
• Draw an arrow representing the first vector
• Now starting at the head of the first arrow, draw a second arrow representing the second vector
• The resultant vector can be found by drawing an arrow going from the tail of the first vector to the tip of the second vector

Diagram showing an example of the “tip-to-tail” addition of two vectors

Author: Jenna

Jenna studied at Cardiff University before training to become a science teacher at the University of Bath specialising in Biology (although she loves teaching all three sciences at GCSE level!). Teaching is her passion, and with 10 years experience teaching across a wide range of specifications – from GCSE and A Level Biology in the UK to IGCSE and IB Biology internationally – she knows what is required to pass those Biology exams.
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