Q. 224.0( 4 Votes )

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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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