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The scalar product of the vector \(\hat{i} + \hat{j} + \hat{k}\) a unit vector along the sum of vectors \(2\hat{i} + 4\hat{j} - 5\hat{k}\; and\; \lambda\hat{i} + 2\hat{j} +3\hat{k}\) is equal to ane. find the value of λ.

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\(\vec{a} = \vec{i} + \vec{j} + \vec{k},\)

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