The scalar product of the vector \( \hat{i}+\hat{j}+\hat{k} \) with...

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The scalar product of the vector \( \hat{i}+\hat{j}+\hat{k} \) with 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 one. Find the value of \( \lambda \).
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