The angle between two vectors

THE ANGLE BETWEEN TWO VECTORSBY WENGO KALUBA L6

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

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

EXAMPLE

PARALLEL VECTORS If a and b are parallel then either:

a.b =ab cos 0 OR a.b = ab cos π

PARALLEL VECTORS For like parallel

vectors:

a.b = ab

For unlike parallel vectors:

a.b = -ab

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

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

IMPORTANT POINT

EXAMPLE

EXAMPLE