Cartesian components

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Example

Sketch the position vectors:

r = 3i + 4j,

r = −2i + 5j,

r = −3i − 2j.

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Slide 13

The modulus of any vector r is equal to its length. As we have noted earlier the modulus of r is usually denoted by |r|. When r = ai + bj the modulus can be obtained using Pythagoras’ theorem. If r is the position vector of point P then the modulus is clearly the distance of P from the origin.

Slide 14

Key Point

if r = ai + bj

then |r| = √(a² + b²)

Slide 15

Point A has coordinates (3, 5). Point B has coordinates (7, 8).

a) Depict these points on a diagram.

b) State the position vectors of A and B.

c) Find an expression for AB.

d) Find |AB|.

Example