Question

Let `veca = hati + hatj + hatk` and `vecb = hatj - hatk`. If `vecc` is a vector such that `veca.vecc = vecb` and `veca.vecc` = 3, then `veca.(vecb.vecc)` is equal to ______.

Options

• –2

• 6

• 2

• –6

Answer 1

Let `veca = hati + hatj + hatk` and `vecb = hatj - hatk`. If `vecc` is a vector such that `veca.vecc = vecb` and `veca.vecc` = 3, then `veca.(vecb.vecc)` is equal to –2.

Explanation:

Given, `veca xx vecc = vecb`

⇒ `-(vecc xx veca) = vecb`

⇒ `vecc xx veca = vecb`

Here, `veca = hati + hatj + hatk` and `vecb = hatj - hatk`

Now, `veca.(vecb xx vecc)`

= `[(veca, vecb, vecc)]`

= `[(vecb, vecc, veca)]`

= `vecb.(vecc xx veca)`

= `vecb.(-vecb)`

= `-|vecb|^2`

= `-(sqrt((1)^2 + (-1)^2))^2`  ...`[(∵ |vecb|  = sqrt((1)^2 + (-1)^2)),(= sqrt(2))]`

= `-(sqrt(2))^2`

= –2