The vector that must be added to the vector $\hat i - 3\hat j + 2\hat k$ and $3\hat i + 6\hat j - 7\hat k$ so that the resultant vector is a unit vector along the $y-$axis is
The vector that must be added to the vector $\hat i - 3\hat j + 2\hat k$ and $3\hat i + 6\hat j - 7\hat k$ so that the resultant vector is a unit vector along the $y-$axis is
$4\hat i + 2\hat j + 5\hat k$
$ - 4\hat i - 2\hat j + 5\hat k$
$3\hat i + 4\hat j + 5\hat k$
Null vector
The vector that must be added to the vector $\hat i - 3\hat j + 2\hat k$ and $3\hat i + 6\hat j - 7\hat k$ so that the resultant vector is a unit vector along the $y-$axis is
Unit vector along y axis $ = \hat j$ so the required vector
$ = \hat j - [(\hat i - 3\hat j + 2\hat k) + (3\hat i + 6\hat j - 7\hat k)]$
$ = - \,4\hat i - \,2\hat j + 5\hat k$
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