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There are two vectors = 2 - 2 and = 7 + 2 - 3 and now we have to express as the sum of two vectors ₁ and ₂ such that ₁ is parallel to and ₂ is perpendicular to .

Let ₁ = p + q + r and ₂ = x + y + z

So, ₁ = λ because both the vectors are parallel to each other and ₂^. = 0 because both the vectors are perpendicular to each.

This is the sum equation.

Taking dot product of on both sides, we get,

18 = 2p – q – 2r,

18 = 4λ + λ + 4λ,

λ = 2.

So, = 4 - 2 - 4

= 3 + 4