For any vector a, show that i-cap x (a x i-cap) + j-cap x (a x j-cap) + k-cap x (a x k-cap) =2a. 

Asked by sunil2791 | 17th Nov, 2017, 07:17: PM

Expert Answer:

begin mathsize 16px style let space straight a equals xi plus yj plus zk
straight i cross times straight i equals 0 comma
straight i cross times straight k equals straight j comma
straight i cross times straight j equals straight k.
similarly space for space straight k space and space straight j
straight i cross times open parentheses straight a cross times straight i close parentheses plus straight j cross times open parentheses straight a cross times straight j close parentheses plus straight k cross times open parentheses straight a cross times straight k close parentheses
equals straight i cross times open parentheses yk plus zj close parentheses plus straight j cross times open parentheses xk plus zi close parentheses plus straight k cross times open parentheses xj plus yi close parentheses
equals yj plus zk plus xi plus zk plus xi plus yk
equals 2 open parentheses xi plus yj plus zk close parentheses
equals 2 straight a end style

Answered by Arun | 5th Dec, 2017, 03:54: PM