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P6 Topic 3: Vectors
Triple scalar product definition backmore
The triple scalar product of the vectors a, b and c is defined to be:
a.b×c
and can be read as the scalar product of a and b×c.
If i, j and k are the familiar unit vectors, then:
If a = a1i+a2j+a3k, b = b1i+b2j+b3k and c = c1i+c2j+c3k then:
a.b×c = a1(b2c3-b3c2)+ a2(b3c1-b1c3) + a3(b1c2-b2c1)
truiple scalar product




Summary

  • The volume of the parallelepiped formed by vectors a, b and c is a.b×c
  • The volume of the tetrahedron formed by vectors a, b and c is 1/6a.b×c
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