The value of \( \vec{b} \) such that scalar product of the vectors \( (\hat{i}+\hat{j}+\hat{k}) ...

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The value of \( \vec{b} \) such that scalar product of the vectors \( (\hat{i}+\hat{j}+\hat{k}) \) with the unit vector parallel to the sum of the vectors \( (2 \hat{i}+4 \hat{j}-5 \hat{k}) \) and \( (b \hat{i}+2 \hat{j}+3 \hat{k}) \) is 1 , is
(1) \( -2 \)
( 5\( )-1 \)
(3) 0
(4) 1
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