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

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

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

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 ${{\rm{\vec B}}}$ ?

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

If $\overrightarrow P \,\,.\,\,\overrightarrow Q = 0\,and\,\overrightarrow P \,\, imes \,\,\overrightarrow Q = 0$, then the angle between $\overrightarrow Q \,and\,\overrightarrow R$ is

$\left( {{\rm{\vec P}} + {\rm{\vec Q}}} \right)$ is a unit vector along X-axis. If ${\rm{\vec P}} = \hat i - \hat j + \hat k,$ then what value is ${\rm{\vec Q}}?$

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

The vector which can give unit vector along x-axis with ${\rm{\vec A}} = 2\hat i - 4\hat j + 7\hat k,\,{\rm{\;\vec B}} = 7\hat i + 2\hat j - 5\hat k$ and ${\rm{\vec C}} = - 4\hat i + 7\hat j + 3\hat k$ is

Find the angle between two vectors $\overrightarrow A = 2\widehat i + \widehat j - \widehat k$ and $\overrightarrow B = \widehat i - \widehat k$

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