Let →a=^i+^j+^k,→b=^i−^j+^k and →c=^i−^j−^k be three vectors. A vector →v in the plane of
→a and →b, whose projection on →c is 1√3, is given by
3^i−^j+3^k
Let →v=→a+λ→b→v=(1+λ)^i+(1−λ)^j+(1+λ)^kProjection of →v on →c=1√3⇒ →v⋅→c|→c|=1√3⇒ (1+λ)−(1−λ)−(1+λ)√3=1√3
⇒1+λ−1+λ−1−λ=1⇒λ−1=1⇒λ=2∴→v=3^i−^j+3^k