If `vecA = 2hati + hatj -3hatk, vecB = hati- 2hatj + hatk` and `vecC = - hati + hatj - 4hatk`, Calculate (i) `vecA.(vecB xx vecC), (ii)vecC (vecAxx vecB), (iii) vecA xx (vecB xx vecC)`

Answer

(i) 20, (ii) 20,(iii)(`8hati -19hatj+ 3 hatk`)

Explanation

(i) `vecA.(vecBxx vecC) = vecA.[(8-1) hati - (-4 + 1) hatj + (1-2) hatk]`
`" "= (2hati + hatj - 3hatk) .(7hati + 3hatj - hatk)=20`
(ii) `vecC.(vecA xx vecB) = vecC.[(6-1)hati - (2+3)hatj +(-4-1)hatk]`
`" "(-hati + hatj - 4hatk).(5hati -5hatj- 5hatk)= 20`
(iii) `vecA xx (vecB xx vecC) = (vecA. vecC) vecB - (vecA. vecB).vecC`
`(11) vecB- (3)vecC = (22 hati - 22hatj+ 11hatk)-(3hati - 3hatj- 12hatk)`
`=8hati- 19hati -hatk`