:The scalar triple product is a special case of a determinant.
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Note that the denominator is the scalar triple product.
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The other pitfall arises when the scalar triple product is positive but the divisor is negative.
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But this is just the scalar triple product, which defines the volume of a parallelepiped.
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The scalar triple product identity follows because each is a different representation of the same diagram's function.
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An example of a pseudoscalar is the scalar triple product ( see vector ), and thus the signed volume.
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One source of potential errors is that the scalar triple product can be negative if,, have the wrong winding.
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Similarly, the scalar triple product is ad hoc, and can instead be expressed uniformly using the exterior product and the geometric product.
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I was answering a question on a third semester calculus exam when I realized a connection between the scalar triple product and the equation for a plane.
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Where parentheses ( * * ) is a scalar product and square brackets [ * * * ] is a scalar triple product, and is an imaginary unit.
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