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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 vectors `vec(b) = 2hat(i) + 4hat(j) - 5hat(k)` and `vec(c ) = lambda hat(i) + 2hat(j) + 3hat(k)` is equal to one. Find the value of `lambda` and hence find the unit vector along `vec(b) + vec(c )`.

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