$\vec{A}$ is a vector quantity such that $|\vec{A}|=$ nonzero constant. Which of the following expressions is true for $\vec{A}$ $?$
$\overrightarrow{ A }\cdot \overrightarrow{ A }=0$
$\overrightarrow{ A } \times \overrightarrow{ A }<0$
$\overrightarrow{ A } \times \overrightarrow{ A }=0$
$\overrightarrow{ A } \times \overrightarrow{ A }>0$
The angle between the two vectors $\vec A = 3\hat i + 4\hat j + 5\hat k$ and $\vec B = 3\hat i + 4\hat j - 5\hat k$ will be....... $^o$
$\vec A$ and $\vec B$ are two vectors and $\theta$ is the angle between them, if $|\vec A \times \vec B|=\sqrt 3(\vec A \cdot \vec B) $ the value of $\theta$ is ......... $^o$
The angle between two vectors $4\hat i + 3\hat j + \hat k$ and $-3\hat i + 2\hat j + 6\hat k$ is ....... $^o$
If $\vec A$ and $\vec B$ are perpendicular vectors and vector $\vec A = 5\hat i + 7\hat j - 3\hat k$ and $\vec B = 2\hat i + 2\hat j - a\hat k.$ The value of $a$ is