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christopher-chibangu
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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