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A vector in the plane of b and c is given by
d = αa + βb
=> d = α(i + j + k) + β(i - j + k)
=> d = i(α + β) + j(α - β) + k(α +β) ...................1
Given length of the projection of d on a = √(2/3)
=> (d . c)/|c| = 1 / √(3)
=> {α + β - α + β -α - β}/{√3} = 1 / √(3)
=> {β - α } = 1
This satisfies when α = 1 and β = 2
From eqaution 1, we get, d
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