Question

If `bara = hati - 2hatj`, `barb = hati + 2hatj, barc = 2hati + hatj - 2hatk`, then find (i) `bara xx (barb xx barc)` (ii) `(bara xx barb) xx barc`. Are the results same? Justify.

Answer 1

(i) `bara xx (barb xx barc)`

`barb xx barc = |(hati, hatj, hatk),(1, 2, 0),(2, 1, -2)|`

= `(-4 - 0)hati - (-2 - 0)hatj + (1 - 4)hatk`

= `-4hati + 2hatj - 3hatk`

∴ `bara xx (barb xx barc) = |(hati, hatj, hatk),(1, -2, 0),(-4, 2, -3)|`

= `(6 - 0)hati - ( -3 - 0)hatj + (2 - 8)hatk`

= `6hati + 3hatj - 6hatk`

(ii) `(bara xx barb) xx barc`

`bara xx barb = |(hati, hatj, hatk),(1, -2, 0),(1, 2, 0)|`

= `(0 - 0)hati - (0 - 0)hatj + (2 - (-2))hatk`

= `4hatk`

∴ `(bara xx barb) xx barc = |(hati, hatj, hatk),(0, 0, 4),(2, 1, -2)|`

= `(0 - 4)hati - (0 - 8)hatj + (0 - 0)hatk`

= `-4hati + 8hatj`

`bara xx (barb xx barc) ≠ (bara xx barb) xx barc`