Consider the following statements:
1. Vectors \(\hat{i}+3\hat{j}+\hat{k}, 2\hat{i}-\hat{j}-\hat{k},7\hat{j}+3\hat{k}\) are parallel to same plane.
2. If \(\overrightarrow{a}\ and \overrightarrow{b}\) are two vectors such that \(|\overrightarrow{a}\times\overrightarrow{b}|=\overrightarrow{a}.\overrightarrow{b}\), then the angle between \(\overrightarrow{a}\ and \overrightarrow{b}\) is \(\frac{\pi }{2}\)
3. \(\hat{i}.(\hat{j}\times \hat{k})+(\hat{i}\times \hat{k}).\hat{j}=2\)
Which of the above statements is/are correct?
1
1 only
2
2 only
3
1 and 2 only
4
1, 2 and 3