Vectors: AS mathematics

1. THE ANGLE
BETWEEN TWO
VECTORS
BY WENGO KALUBA L6

2.  The angle between two vector is defined as the angle formed
between two vectors when they converge (come together) or
diverge (move apart)

3. THE SCALAR PRODUCT
 The scalar product is written as a.b and is defined by the following
formula :
• The scalar product is commutative, meaning that a.b = b.a

4. EXAMPLE

5. PARALLEL VECTORS
 If a and b are parallel then either:
a.b =ab cos 0 OR a.b = ab cos π

6. PARALLEL VECTORS
 For like parallel
vectors:
a.b = ab
 For unlike
parallel vectors:
a.b = -ab

7. PERPENDICULAR VECTORS
• The scalar product for any set of
perpendicular vectors is 0, i.e.
• a.b = 0
• This is because cos90 = 0 no matter what
the values of a and b are
• For the unit vectors i, j and k, this
means i.j = j.k = k.i = 0

8. SCALAR PRODUCT IN CARTESIAN
FORM (IN TERMS OF i, j and k)
 a = x1i + y1j + z1k and b = x2i + y2j + z2k
 a.b = (x1x2 + y1y2 + z1z2)
 e.g.
(2i - 3j + 4k) . (i + 3j – 2k) = (2)(1) + (-3)(3) + (4)(-2)
=-15

9. IMPORTANT POINT

10. EXAMPLE

11. EXAMPLE