If a and b are unit vectors, then which of the following value of a b is NOT possible

Step-by-step solution

Given that a and b are unit vectors, their magnitudes are | a | = 1 and | b | = 1 . The dot product of two vectors is defined as a b = | a | | b | , where is the angle between the vectors. Substituting the magnitudes, we get a b = (1)(1) = . Since the range of the cosine function is [-1, 1] , the value of a b must satisfy -1 a b 1 . Checking the given options: Option (1): - 1 2 is in [-1, 1] . Option (2): 3 2 0.866 is in [-1, 1] . Option (3): 1 3 0.577 is in [-1, 1] . Option (4): 3 1.732 , which is greater than 1.