Given that $\overrightarrow A + \overrightarrow B + \overrightarrow C= 0$ out of three vectors two are equal in magnitude and the magnitude of third vector is $\sqrt 2 $ times that of either of the two having equal magnitude. Then the angles between vectors are given by

If $\vec{P}+\vec{Q}=\overrightarrow{0}$, then which of the following is necessarily true?

If the resultant of $n$ forces of different magnitudes acting at a point is zero, then the minimum value of $n$ is

If two vectors $2\hat i + 3\hat j - \hat k$ and $ - 4\hat i - 6\hat j + \lambda \hat k$ are parallel to each other then value of $\lambda$ be

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

The five sides of a regular pentagon are represented by vectors $A _1, A _2, A _3, A _4$ and $A _5$, in cyclic order as shown below. Corresponding vertices are represented by $B _1, B _2, B _3, B _4$ and $B _5$, drawn from the centre of the pentagon.Then, $B _2+ B _3+ B _4+ B _5$ is equal to