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

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

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:

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

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

If $\overrightarrow P \,\,.\,\,\overrightarrow Q = 0\,and\,\overrightarrow P \,\, imes \,\,\overrightarrow Q = 0$, then the angle between $\overrightarrow Q \,and\,\overrightarrow R$ 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 angle between the two vectors $\overrightarrow A = \widehat i + 2\widehat j - \widehat k\,and\,\overrightarrow B = - \widehat i + \widehat j - 2\widehat k$ 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

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