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Let (R 3 , ×) be the set of 3d vectors equipped with the operation of...

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Basic Math

Let (R 3 , ×) be the set of 3d vectors equipped with theoperation of vector crossproduct. Which of the following propertiesdoes this operation satisfy (give proofs in all cases)?

(a) has identity element(s)? (If so, determine all identityelements.)

(b) has idempotent element(s)? (If so, determine all idempotentelements.)

(c) commutative?

(d) associative?

Answer & Explanation Solved by verified expert
3.9 Ratings (608 Votes)
a let M abc and N pqr be 2 arbitrary vectors in R3 Then M x N brcqcparaqbp Now if M x N M then we must have brcq a cpar b and aqbp c which need not be true    See Answer
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