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Vector Algebra — Part 1: Vectors, components and the section formula

Beta

Lesson

Vector Algebra, Part 1

Quantities that need a size and a direction.

In this lesson you will

Tell vectors from scalars and name the types of vectors
Find the magnitude, unit vector and direction cosines of a vector
Add vectors by the triangle and parallelogram laws and multiply by scalars
Use position vectors and the section formula

The vector $\vec{a} = \overrightarrow{AB}$: its length is the magnitude $|\vec{a}|$, the arrow gives the direction.

Concept

Scalars and vectors

A scalar is fully described by a number with a unit. A vector needs a magnitude and a direction.

Ask: does the quantity need a direction to make sense?
Scalar (size only)	Vector (size and direction)
mass $5$ kg	displacement $3$ km north-east
temperature $30°$ C	velocity $60$ km/h due east
time $2$ h	force $10$ N downwards
speed $40$ km/h	acceleration $9.8$ m/s $^2$ downwards