If \( \vec{a} \) and \( \vec{b} \) are unit vectors, then which of the following values of \( \vec{a}.\vec{b} \) is not possible ?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \sqrt{2} \)
For unit vectors, \( |\vec{a}|=|\vec{b}|=1 \), so
\( \displaystyle \vec{a}\cdot\vec{b}=|\vec{a}||\vec{b}|\cos\theta=\cos\theta \)
Hence \( \vec{a}\cdot\vec{b} \) always lies in [−1, 1]. Since \( \sqrt{2}\gt 1 \), the value \( \sqrt{2} \) is not possible. The other three values lie in [−1, 1].