the angle between two vectors
TRANSCRIPT
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THE ANGLE BETWEEN TWO VECTORSBY WENGO KALUBA L6
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The angle between two vector is defined as the angle formed between two vectors when they converge (come together) or diverge (move apart)
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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
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EXAMPLE
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PARALLEL VECTORS If a and b are parallel then either:
a.b =ab cos 0 OR a.b = ab cos π
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PARALLEL VECTORS For like parallel
vectors:
a.b = ab
For unlike parallel vectors:
a.b = -ab
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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
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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
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IMPORTANT POINT
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EXAMPLE
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EXAMPLE