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The scalar product of the vector vec a=...

The scalar product of the vector ` vec a= hat i+ hat j+ hat k` with a unit vector along the sum of the vectors ` vec b=2 hat i+4 hat j-5 hat k\ a n d\ vec c=lambda hat i+2 hat j+3 hat k` is equal to 1. Find the value of `lambda` and hence find the unit vector along ` vec b+ vec cdot`

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