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Find a vector of magnitude 4 units which is parallel to the vector \(\sqrt3\hat i+\hat j\)

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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 \(2\sqrt3\hat i+2\hat j.\)

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