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The scalar product of the vector a = i + j + k with a unit vector along the sum of vectors b = 2 i + 4 j - 5 k and vector c = λi + 2 j + 3 k

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The scalar product of the vector a = i + j + k with a unit vector along the sum of vectors b = 2 i + 4 j - 5 k and vector c = λi + 2 j + 3 k is equal to one. Find the value of λ and hence find the unit vector along |vector (b + c)| = 7.

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Given vector

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