Answer :

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

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