hexaedru8p

hexaedru8p

Answered

2022-10-09

If a and c are unit vectors at an angle π / 3 with each other and ( a × ( b × c ) ) . ( a × c ) = 5, then what is the value of [a b c]? I just know the basic meaning of what are vector and scalar triple product. How do I do this question?

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Answer & Explanation

Salma Baird

Salma Baird

Expert

2022-10-10Added 8 answers

We want to compute a b × c = b a × c. We'll use a × ( b × c ) = ( a c ) b ( a b ) c so
5 = ( a × ( b × c ) ) ( a × c ) = ( a c ) ( b a × c ) .
Hence
[ a b c ] = 5 a c = 5 cos π 3 = 10.

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Shawn Peck

Shawn Peck

Expert

2022-10-11Added 2 answers

Use a × ( b × c ) = ( a c ) b ( a b ) c. Then
( a × ( b × c ) ) ( a × c ) = ( a c ) b ( a × c ) ( a b ) c ( a × c ) = ( a b ) [ a , b , c ]
etc.

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