If $\vec{A} = 2\hat{i} + 3\hat{j} - \hat{k}$ and $\vec{B} = \hat{i} + \hat{j} + \hat{k}$, find the projection of $\vec{A}$ on $\vec{B}$.

Two vectors $\vec{A}$ and $\vec{B}$ have magnitudes A and B respectively. If $\vec{A} \cdot \vec{B} = -AB$, and neither A nor B is zero, which of the following is true about the angle $heta$ between the vectors?

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

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 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

${\rm{\vec A}} = 3\hat i - \hat j + 7\hat k\,and\,{\rm{\vec B}} = 5\hat i - \hat j + 9\hat k$ 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

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

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

For two vectors $\vec{A}$ and $\vec{B}$, if $|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|$, what is the angle between $\vec{A}$ and $\vec{B}$?