Скалярное произведение векторов, угол между векторами

1. Скалярное произведение векторов, угол между векторами

Higher
Outcome 1
www.mathsrevision.com
Тема урока
Скалярное произведение
векторов, угол между
векторами

2.

The scalar product
Higher
Outcome 1
Must be
www.mathsrevision.com
The scalar product is defined
being:
tail as
to tail
a
a b a b cos
0 180
0
θ
b

3.

Component Form Scalar Product
Outcome 1
www.mathsrevision.com
Higher
If
a1
b1
a a2 and b b2 then
a
b
3
3
a b a1b1 a2b2 a3b3

4.

Angle between Vectors
Outcome 1
www.mathsrevision.com
Higher
To find the angle between two vectors we simply
use the scalar product formula rearranged
a b
cos =
a b
or
a1b1 a2b2 a3b3
cos =
ab

5.

Perpendicular Vectors
Outcome 1
www.mathsrevision.com
Higher
Given a 0 and b 0 and a b 0
Then
a b
0
cos =
0
a b a b
= cos (0) = 90
-1
o
If a . b = 0 then a and b are perpendicular

6.

Properties of a Scalar Product
Higher
Outcome 1
www.mathsrevision.com
Two properties that you need to be aware of
a b b a
a (b c) a b a c