In coordinate space, consider two vectors $\vec{u}$ and $\vec{v}$ satisfying the dot product $\vec{u} \cdot \vec{v} = \sqrt{15}$ and the cross product $\vec{u} \times \vec{v} = (-1, 0, 3)$. Select the correct options. (1) The angle $\theta$ between $\vec{u}$ and $\vec{v}$ (where $0 \leq \theta \leq \pi$, $\pi$ is the circumference ratio) is greater than $\frac{\pi}{4}$ (2) $\vec{u}$ could be $(1, 0, -1)$ (3) $|\vec{u}| + |\vec{v}| \geq 2\sqrt{5}$ (4) If $\vec{v}$ is known, then $\vec{u}$ can be uniquely determined (5) If $|\vec{u}| + |\vec{v}|$ is known, then $|\vec{v}|$ can be uniquely determined
In coordinate space, consider two vectors $\vec{u}$ and $\vec{v}$ satisfying the dot product $\vec{u} \cdot \vec{v} = \sqrt{15}$ and the cross product $\vec{u} \times \vec{v} = (-1, 0, 3)$. Select the correct options.\\
(1) The angle $\theta$ between $\vec{u}$ and $\vec{v}$ (where $0 \leq \theta \leq \pi$, $\pi$ is the circumference ratio) is greater than $\frac{\pi}{4}$\\
(2) $\vec{u}$ could be $(1, 0, -1)$\\
(3) $|\vec{u}| + |\vec{v}| \geq 2\sqrt{5}$\\
(4) If $\vec{v}$ is known, then $\vec{u}$ can be uniquely determined\\
(5) If $|\vec{u}| + |\vec{v}|$ is known, then $|\vec{v}|$ can be uniquely determined