Question

Let `veca = hati - 2hatj + 3hatk, vecb = hati + hatj + hatk` and `vecc` be a vector such that `veca + (vecb xx vecc) = vec0` and `vecb.vecc` = 5. Then, the value of `3(vecc.veca)` is equal to ______.

पर्याय

• 0

• 1

• 2

• 3

Answer 1

Let `veca = hati - 2hatj + 3hatk, vecb = hati + hatj + hatk` and `vecc` be a vector such that `veca + (vecb xx vecc) = vec0` and `vecb.vecc` = 5. Then, the value of `3(vecc.veca)` is equal to 0.

Explanation:

`veca = hati - 2hatj + 3hatk`

`vecb = hati + hatj + hatk`

Now, `veca.vecb` = 1 – 2 + 3 = 2 ...(i)

Also, given `veca + (vecb xx vecc)` = 0

⇒ `veca = -(vecb xx vecc)`

⇒ `veca.vecb = -(vecb xx vecc).vecb` ...(ii)

Equation (i) and equation (ii) are contradicting.