Let \(\vec a\) be the required vector that is parallel to \(\sqrt3\hat i+\hat j.\)
We know any vector parallel to a given vector \(\text x\hat i+y\hat j\) is of the form \(\lambda(\text x \hat i+y\hat j),\)where λ is a real number.
⇒ \(\vec a=\lambda(\sqrt3\hat i+\hat j)\)
Now, we need to find λ such that |\(\vec a\)| = 4.
Recall the magnitude of the vector \(\text x\hat i+y\hat j\) is given as
Squaring both the sides, we have
Thus, the required vector is \(2\sqrt3\hat i+2\hat j.\)