Question

If `veca = hati + 2hatj + 3hatk, vecb = 2hati + 3hatj + hatk, vecc = 3hati + hatj + 2hatk` and `αveca + βvecb + γvecc = -3(hati - hatk)`, then the ordered triplet (α, β, γ) is ______.

Options

• (2, –1, –1)

• (–2, 1, 1)

• (–2, –1, 1)

• (2, 1, –1)

Answer 1

If `veca = hati + 2hatj + 3hatk, vecb = 2hati + 3hatj + hatk, vecc = 3hati + hatj + 2hatk` and `αveca + βvecb + γvecc = -3(hati - hatk)`, then the ordered triplet (α, β, γ) is (2, –1, –1).

Explanation:

Equating the components in

`α(hati + 2hatj + 3hatk) + β(2hati + 3hatj + hatk) + γ(3hati + hatj + 2hatk)`

= `-3(hati - hatk)`, we have

α + 2β + 3γ = –3  ....(i)

2α + 3β + γ = 0  .....(ii)

3α + β + 2γ = 3  .....(iii)

Solving the equations (i), (ii), and (iii), we get

α = 2, β = –1, γ = –1.