Question

If a = `veca = hati + hatj - 2hatk, vecb = 2hati - hatj + hatk` and `vecc = 3hati - hatk` and `vecc = mveca + nvecb`, then m + n is equal to ______.

Options

• 0

• 1

• 2

• –1

Answer 1

If a = `veca = hati + hatj - 2hatk, vecb = 2hati - hatj + hatk` and `vecc = 3hati - hatk` and `vecc = mveca + nvecb`, then m + n is equal to 2.

Explanation:

Given, `veca = hati + hatj - 2hatk, vecb = 2hati - hatj + hatk, vecc = 3hati - hatk` and `vecc = mveca + nvecb`

As, `3hati - hatk = m(hati + hatj - 2hatk) + n(2hati - hatj + hatk)`

`\implies 3hati - hatk = (m + 2n)hati + (m - n)hatj + (-2m + n)hatk`

After equating the coefficient of `hati, hatj` and `hatk`, on both sides respectively, we get

3 = m + 2n, 0 = m – n and –1 = –2m + n

`\implies` 3 = n + 2n

3 = 3n

`3/3` = n

`\implies` n = 1

`\implies` m = 1 and n = 1

`\implies` m + n

= 1 + 1

= 2