Question

If `veca = 3hati + 2hatj + 4hatk, vecb = hati + hatj - 3hatk` and `vecc = 6hati - hatj + 2hatk` are three given vectors, then `(2veca.hati)hati - (vecb.hatj)hatj + (vecc.hatk)hatk` is the same as the vector ______.

विकल्प

• `veca`

• `vecb + vecc`

• `veca - vecb`

• `vecc`

Answer 1

If `veca = 3hati + 2hatj + 4hatk, vecb = hati + hatj - 3hatk` and `vecc = 6hati - hatj + 2hatk` are three given vectors, then `(2veca.hati)hati - (vecb.hatj)hatj + (vecc.hatk)hatk` is the same as the vector `underlinebb(vecc)`.

Explanation:

`2veca.hati = 2(3hati + 2hatj + 4hatk).hati`

= `(6hati + 4hatj + 8hatk).hati`

= 6

`vecb.hatj = (hati + hatj - 3hatk).hatj`

= 1

`vecc.hatk = (6hati - hatj + 2hatk).hatk`

= 2

`(2veca.hati)hati - (vecb.hatj)hatj + (vecc.hatk)hatk`

= `6hati - hatj + 2hatk`

= `vecc`