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Sir, plz explain vector triple product?

Sir, plz explain vector triple product?

Grade:12

1 Answers

Askiitian.Expert Rajat
24 Points
13 years ago

Hi,

The vector triple product

If A, B and C are three vectors, then we can combine them in this way:

Ax(BxC)

to get a vector result, which is known as the vector triple product.

As you know, the cross product is calculated using a determinant and we can extend this to Ax(BxC) to get a rather more complicated determinant than the scalar triple product gave us, again involving all three vectors.

However there is a much simpler way to evaluate a vector triple product, because it can be shown that this is true:

Ax(BxC)=(A.C)B-(A.B)C

and

(AxB)xC=(C.A)B-(C.B)A.

So we can evaluate either of those right-hand sides instead, which do not involve any determinants. However you do need to remember them!

 

Regards,

Rajat

askiitian Expert

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