Concept:Properties of the cross product of vectora × b is a vector that is perpendicular to both a and b.The direction of a × b is determined by the right-hand rule. (This means that if we curl the fingers of the right hand from a to b, then the thumb points in the direction of (a × b)).The magnitude (or length) of the vector a × b, written as ?a × b?b × a = ? a × b and a × a = 0Calculation:Statement I: \(\vec a\) is unique if \(\vec b\) and \(\vec c\) are givenIf \(\displaystyle \vec b\ and \ \vec c\) are given, then vector a is determined by the right-hand rule which is perpendicular to both \(\displaystyle \vec b\ and \ \vec c\)As \(\displaystyle \vec b\ and \ \vec c\) is given, the magnitude of \(\displaystyle \vec b\ and \ \vec c\) is also given.So, we can say that \(\displaystyle \vec a\) is unique whose magnitude and direction are dependent on \(\displaystyle \vec b\ and \ \vec c\)Thus, a statement I is correct.Statement II: \(\vec c\) is unique if \(\vec a\) and \(\vec b\) are givenIf \(\displaystyle \vec a\ and \ \ \vec b\) are known then the resultant is perpendicular to both a and b which is given the right-hand rule.The magnitude of the vector a × b, written as ?a × b?. As a and b are given, magnitude is unique.So, we can say that \(\displaystyle \vec c\) is unique whose magnitude and direction are dependent on \(\displaystyle \vec a \ and \ \vec b\)Thus, statement II is correct.? Both statements I and II are correct.