Read the two statements and choose the correct option.

I. The vector product of two unit vectors is always a unit vector.

II. If $\vec{a} \times \vec{b} = \vec{a} \times \vec{c}$ and $\vec{a} \ne \vec{0}$, then $\vec{b} = \vec{c}$.

Explanation

1. 01

   I: $\lvert \hat{a} \times \hat{b} \rvert = \sin \theta$, which is 1 only for perpendicular vectors; $\hat{i} \times \hat{i} = \vec{0}$. False.

2. 02

   II: $\vec{a} \times (\vec{b} - \vec{c}) = \vec{0}$ only says $\vec{b} - \vec{c}$ is parallel to $\vec{a}$; for example $\hat{i} \times \hat{j} = \hat{i} \times (\hat{i} + \hat{j})$. False.