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Question:

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;

^i−^j+3^k

−^i−^j−^k

^i+3^j−^k

3^i−^j+3^k

Solution:

Let →v=λα+μβ→v=(λ+μ)^i+(λ−μ)^j+(λ+μ)^kProjection of →v on →c=→v.→c∣∣→c∣∣=1√3→(λ+μ)−(λ−μ)−(λ+μ)√3=1√3→μ−λ=1orμ=λ+1→→v=(2λ+1)^i−^j+(2λ+1)^kFor λ=1,→v=3^i−^j+3^k