Given That $\vec { v }$ And $\vec { w }$ Are Non-Zero Vectors and That

Given that $\vec { v }$ and $\vec { w }$ are non-zero vectors and that $\vec { v } \cdot \vec { w } = 0$ and $\vec { v } \times \vec { w } = \vec { i } + \vec { j } + \vec { k }$ , then which of the following MUST be true? Select all that apply.

A) $\vec { v }$ is perpendicular to $\vec { w }$ .
B) $\vec { v }$ is parallel or anti-parallel to $\vec { w }$ .
C) The angle $\theta$ between
$\vec { v }$ and
$\vec { w }$ satisfies
.
D) The angle $\theta$ between
$\vec { v }$ and
$\vec { w }$ satisfies
.
E) At least one of $\| \vec { v } \|$ and
$\| \vec { w } \|$ is greater than 1.