If \(\vec{a}\ =\ \hat{i}\ +\ 2\hat{j}\ +\ 2\hat{k}\) and \(\vec{b}\ =\ 3\hat{i}\ +\ 5\hat{j}\ +\ \sqrt{2}\hat{k}\) then a vector in the direction of \(\vec{a}\) and having magnitude as \(|\vec b|\) is
1
\(\frac{1}{2}(3 \hat{i}\ +\ 5\hat{j}\ +\ \hat{k})\)
2
\(2( \hat{i}\ -\ 2\hat{j}\ +\ 2\hat{k})\)
3
\(\frac{1}{2}(3 \hat{i}\ -\ 5\hat{j}\ +\ \hat{k})\)
4
\(2( \hat{i}\ +\ 2\hat{j}\ +\ 2\hat{k})\)