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 ....... $units^2$.

Consider two vectors $\vec{F}_1 = 2\hat{i} + 5\hat{k}$ and $\vec{F}_2 = 3\hat{j} + 4\hat{k}$. The magnitude of the scalar product of these vectors is

If $\overrightarrow{F}=(4 \hat{i}-10 \hat{j}) \text{ N}$ and $\overrightarrow{r}=(-5 \hat{i}-3 \hat{j}) \text{ m}$,then $(\overrightarrow{r} \times \overrightarrow{F})$ is

Calculate the values of $a$ and $b$ if vectors $a\hat{i} + b\hat{j} = \hat{n}$ and $(\hat{i} + \hat{j})$ are perpendicular to each other. Note: $\hat{n}$ is a unit vector.

If $|\overrightarrow{A}|=4$ unit,$|\overrightarrow{A}+\overrightarrow{B}|=10$ unit and $\overrightarrow{A} \cdot(\overrightarrow{A}+\overrightarrow{B})=20$ unit,then $|\overrightarrow{B}|=$ ?

What is the product of two vectors if they are parallel or antiparallel?