Two equal forces ($P$ each) act at a point inclined to each other at an angle of $120^°$. The magnitude of their resultant is

Two vectors having equal magnitudes of $x\, units$ acting at an angle of $45^o$ have resultant $\sqrt {\left( {2 + \sqrt 2 } \right)} $ $units$. The value of $x$ is

Two forces $\vec{F}_1$ and $\vec{F}_2$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $\vec{F}_1$ and $\overrightarrow{\mathrm{F}}_2$ is $\cos ^{-1}\left(\frac{1}{\mathrm{n}}\right)$. The value of $|\mathrm{n}|$ is__________.

How many minimum number of non-zero vectors in different planes can be added to give zero resultant

The three vectors $\overrightarrow A = 3\hat i - 2\hat j + \hat k,\,\,\overrightarrow B = \hat i - 3\hat j + 5\hat k$ and $\overrightarrow C = 2\hat i + \hat j - 4\hat k$ form

The vectors $\vec{A}$ and $\vec{B}$ are such that

$|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$

The angle between the two vectors is