Why is (vec(b) xx vec(a)) xx vec(b) non zero?

mangicele4s

mangicele4s

Answered question

2022-09-25

If I use the rule of vector triple product, it becomes:
b × a × b = a ( | b | 2 ) b ( b a )
which is generally non-zero, but suppose I use properties of cross product:
a × b = b × a
Hence,
b × a × b = a × b × b = a × ( b × b ) = 0
What did I do wrong?

Answer & Explanation

Klecanlh

Klecanlh

Beginner2022-09-26Added 11 answers

Removing the parenthesis makes you perform invalid transformations, because the cross product is not associative.
In fact
a × b × c
has no defined meaning.
Unless a , b are parallel, b × a is orthogonal to b , hence not parallel, and ( b × a ) × b is nonzero.
Gillian Cooper

Gillian Cooper

Beginner2022-09-27Added 3 answers

S = P × ( Q × R ) = ( P . R ) Q ( P . Q ) R
So ( b × a ) × b = b × ( b × a ) = [ ( b . a ) b ( b . b ) a ] 0

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