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34`2sqrt2`6

Answer :

bSolution :

`|veca + vecb + 3 vecc |^(2) = 16` <br> `Rightarrow |veca|^(2) + |vecb|^(2) + 9 |vecc|^(2) + 2cos theta_(1) + 6 cos theta_(2)` <br> ` + 6 cos theta_(3) = 16, theta_(3) ne [ pi//6, 2pi//3]` <br> `or 2 cos theta_(1)+ 6 cos theta_(2) = 5-6 cos theta_(3)` <br> ` or ( cos theta_(1) + 3 costheta_(2))_(max) = 4` **Two type of numbers - Vector and scalar.**

**Evolution of vector concept**

**Representation of vector direction sense magnitude of vector or length**

**Equal vectors, null vector, unit vectors, position vector, like and unlike vectors,collinear and parallel vectors**

**Co-initial vectors, coterminous vector and co-planar vectors,negative of a vector,reciprocal vectors**

**Free vector and localized vector**

**In a regular hexagon find which vectors are collinear, equal, coinitial, collinear but not equal.**

**Parallelogram law of addition of vectors**

**Properties of addition of vectors**

**Magnitude of addition of two vectors**