Vector $\vec A$ has magnitude of 5 unit directed along east, then vector $6\vec A$

Dot product of two vectors $\overrightarrow A = \widehat i + 3\widehat j - 2\widehat k\,and\,\overrightarrow B = 3\widehat i - \widehat j + 4\widehat k$ is

The X and Y components of vector ${\rm{\vec A}}$ have numerical values 6 and 6 respectively and that of $\left( {{\rm{\vec A}} + {\rm{\vec B}}} \right)$ have numerical values 10 and 9. What is the numerical value of ${{\rm{\vec B}}}$ ?

The adjacent sides of a parallelogram are represented by co-initial vectors $2\hat i + 3\hat j\,and\,\hat i + 4\hat j$. The area of the parallelogram is

Velocity and acceleration vectors of a charged particle moving perpendicular to the direction of magnetic field at a given instant of time are $\overrightarrow V = 2\widehat i + c\widehat j\,and\,\overrightarrow a = 3\widehat i + 4\widehat j$ respectively. Then the value of ‘C’ is

If the resultant of the vectors $\left( {\hat i + 2\hat j - \hat k} \right),\left( {\hat i - \hat j + 2\hat k} \right)$ and ${\rm{\vec C}}$ is a unit vector along the y-direction, then ${\rm{\vec C}}$ is

${\rm{\vec A}} = 3\hat i - \hat j + 7\hat k\,and\,{\rm{\vec B}} = 5\hat i - \hat j + 9\hat k$ the direction cosine m of the vector ${\rm{\vec A}} + {\rm{\vec B}}$ is

$\overrightarrow A \,.\,\overrightarrow B = - \left| A \right|\left| B \right|$, then

${\rm{\vec A}} = 3\hat i - \hat j + 7\hat k\,and\,{\rm{\vec B}} = 5\hat i - \hat j + 9\hat k$ the direction cosine m of the vector ${\rm{\vec A}} + {\rm{\vec B}}$ is

Velocity and acceleration vectors of a charged particle moving perpendicular to the direction of magnetic field at a given instant of time are $\overrightarrow V = 2\widehat i + c\widehat j\,and\,\overrightarrow a = 3\widehat i + 4\widehat j$ respectively. Then the value of ‘C’ is

A force is inclined at ${60^0}$ to the horizontal. If its rectangular component in the horizontal direction is 50 N, then magnitude of the force in the vertical direction is