NDA 2021 Mathematics question
Consider the following statements : 1. The cross product of two unit vectors is always a unit vector. 2. The dot product of two unit vectors is always unity. 3. The magnitude of sum of two unit vectors is always greater than the magnitude of their difference. Which of the above statements are **not** correct?
Answer: (D)
Solution
Let and be unit vectors with angle between them. Statement 1: , which is 1 only when ; so it is not always a unit vector. Not correct. Statement 2: , which is 1 only when .
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