The resultant of two vector of equal magnitude is twice of magnitude of either of the vectors the angle between them is

The resultant of two vector of equal magnitude is twice of magnitude of either of the vectors the angle between them is

What is the angle between $\hat i + 2\hat j + 2\hat k\,and\,\,\hat i$

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

The component of $\overrightarrow A$ along $\overrightarrow B$ is 2 times that of the component of $\overrightarrow B$ along $\overrightarrow A$. Then A : 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 $\overrightarrow A = 2\hat i + 3\hat j + 4\hat k\,\,and\,\,{\rm{\vec B}} = 4\hat i + 3\hat j + 2\hat k$, then angle between $\overrightarrow A$ and ${\rm{\vec B}}$ is

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

Projection of ${\rm{\vec P}}\,{\rm{on}}\,{\rm{\vec Q}}\;$ is

The angle between the z-axis and the vector $\hat i + \hat j + \sqrt 2 \hat k$ is

The vectors ${\rm{\vec a}}\,and\,{\rm{\vec b}}$ are such that $\left| {{\rm{\vec a}} + {\rm{\vec b}}} \right| = \left| {{\rm{\vec a}} - {\rm{\vec b}}} \right|$. What is the angle between ${\rm{\vec a}}\,and\,{\rm{\vec b}}$ ?