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 ${\rm{\vec A}}$

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

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

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

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

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

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

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

What is the numerical value of the vector $3\hat i + 4\hat j + 5\hat k?$