NEET Chemistry Structure Of Atom Scalar Product (Or) Dot Product MCQs

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

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

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 ${\rm{\vec A}}$

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 ${\rm{\vec A}}$

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

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 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

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

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