For any two non-zero vectors $\vec{A}$ and $\vec{B}$, if $|\vec{A} imes \vec{B}| = \vec{A} \cdot \vec{B}$, the angle between $\vec{A}$ and $\vec{B}$ is:

If ${\rm{\vec A}}{\rm{.\vec B}} = AB,$, then the angle between ${\rm{\vec A}}\,{\rm{and}}\,{\rm{\vec B}}$ is

If  ${\rm{\vec P}} = 4{\rm{\hat i}} - 2{\rm{\hat j}} + 6{\rm{\hat k\;}}\,\,\,{\rm{and}}\,\,{\rm{\vec Q}} = {\rm{\hat i}} - 2{\rm{\hat j}} - 3{\rm{\hat k}}$ , then the angle which ${\rm{\vec P}} + {\rm{\vec Q}}$ makes with x-axis is

If two vectors $\vec{A}$ and $\vec{B}$ are parallel to each other, what is the magnitude of their cross product?

If $\overrightarrow {{a_1}}$ and $\overrightarrow {{a_2}}$ are two non collinear unit vectors inclined at ${60^0}$ to each other then the value of $\left( {\overrightarrow {{a_1}} - \overrightarrow {{a_2}} } \right).\left( {\overrightarrow {2{a_1}} + \overrightarrow {{a_2}} } \right)$

If $\overrightarrow A = 2\hat i + 3\hat j + 4\hat k\,\,and\,\,{\rm{\vec B}} = 4\hat i + 3\hat j + 2\hat k$, then angle between $\overrightarrow A$ and ${\rm{\vec B}}$ is

The vector projection of a vector $3\widehat i + 4\widehat k$ on y-axis is

If $\overrightarrow A = 2\hat i + 3\hat j + 4\hat k\,\,and\,\,{\rm{\vec B}} = 4\hat i + 3\hat j + 2\hat k$, then angle between $\overrightarrow A$ and ${\rm{\vec B}}$ is

The angle between ${\rm{\vec A}}\;\,and\,{\rm{\vec B}}\,is\,heta$, the value of the triple product ${\rm{\vec A}}{\rm{.\vec B}} imes {\rm{\vec A}}$ is

If  ${\rm{\vec P}} = 4{\rm{\hat i}} - 2{\rm{\hat j}} + 6{\rm{\hat k\;}}\,\,\,{\rm{and}}\,\,{\rm{\vec Q}} = {\rm{\hat i}} - 2{\rm{\hat j}} - 3{\rm{\hat k}}$ , then the angle which ${\rm{\vec P}} + {\rm{\vec Q}}$ makes with x-axis is

If $\overrightarrow A = 2\hat i + 3\hat j + 4\hat k\,\,and\,\,{\rm{\vec B}} = 4\hat i + 3\hat j + 2\hat k$, then angle between $\overrightarrow A$ and ${\rm{\vec B}}$ is