If a particle moves from point $P (2,3,5)$ to point $Q (3,4,5)$. Its displacement vector be

The magnitude of vector $\overrightarrow A ,\,\overrightarrow B $ and $\overrightarrow C $ are respectively $12, 5$ and $13$ units and $\overrightarrow A + \overrightarrow B = \overrightarrow C $ then the angle between $\overrightarrow A $ and $\overrightarrow B $ is

The vector that must be added to the vector $\hat i - 3\hat j + 2\hat k$ and $3\hat i + 6\hat j - 7\hat k$ so that the resultant vector is a unit vector along the $y-$axis is

The maximum and minimum magnitude of the resultant of two given vectors are $17 $ units and $7$ unit respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is

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

For the resultant of the two vectors to be maximum, what must be the angle between them....... $^o$