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

The sum of two vectors ${\rm{\vec A}}\,and\,{\rm{\vec B}}$ is at right angles to their difference. Then

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

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

A vector ${\rm{\vec A}}$ when added to the vector ${\rm{\vec B = }}3\hat i + 4\hat j$ yields a resultant vector that is in the positive y direction and has a magnitude equal to that of ${\rm{\vec B}}$ Find the magnitude of ${\rm{\vec A}}$

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

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

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is:

Find the vector component of vector $\overrightarrow A = 2\widehat i + 3\widehat j$ along the direction of $\overrightarrow B = \widehat i + \widehat j$

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

What is the angle between ${\rm{\vec P}}\,and\,{\rm{\vec Q}}$. The resultant of $\left( {{\rm{\vec P}} + {\rm{\vec Q}}} \right)\,and\,\left( {{\rm{\vec P}} - {\rm{\vec Q}}} \right)?$