The area of the parallelogram represented by the vectors $\overrightarrow A = 2\hat i + 3\hat j$ and $\overrightarrow B = \hat i + 4\hat j$ is ....... $units^2$.

For any two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$,if $\overrightarrow{A} \cdot \overrightarrow{B} = |\overrightarrow{A} \times \overrightarrow{B}|$,the magnitude of $\overrightarrow{C} = \overrightarrow{A} + \overrightarrow{B}$ is equal to

If the component of the vector $\vec{A}$ along the vector $\vec{B}$ is twice the component of $\vec{B}$ along $\vec{A}$, then the ratio of magnitudes of vectors $\vec{A}$ and $\vec{B}$ is

If vectors $\overrightarrow {A} = \cos\omega t\hat i + \sin\omega t\hat j$ and $\overrightarrow {B} = \cos\frac{\omega t}{2}\hat i + \sin\frac{\omega t}{2}\hat j$ are functions of time,then the value of $t$ at which they are orthogonal to each other is:

Find the angle between two vectors $\vec A = 2\hat i + \hat j - \hat k$ and $\vec B = \hat i - \hat k$ in degrees.

Show that the area of the triangle formed by the vectors $\vec{a}$ and $\vec{b}$ is one-half of the magnitude of $\vec{a} \times \vec{b}$.