List of top Mathematics Questions on Vectors asked in KCET

The vectors $\overrightarrow{AB} = 3\hat{i} + 4\hat{k}$ and $\overrightarrow{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}$ are the sides of a $\triangle ABC$. The length of the median through $A$ is:

Let $\vec{a}$ and $\vec{b}$ be two unit vectors and $\theta$ is the angle between them. Then $\vec{a} + \vec{b}$ is a unit vector if:

If $\vec{a}, \vec{b}, \vec{c}$ are three non-coplanar vectors and $\vec{p}, \vec{q}, \vec{r}$ are vectors defined by:}\\ \[ \vec{p} = \frac{\vec{a} \times \vec{c}}{[\vec{a} \, \vec{b} \, \vec{c}]}, \quad \vec{q} = \frac{\vec{c} \times \vec{b}}{[\vec{a} \, \vec{b} \, \vec{c}]}, \quad \vec{r} = \frac{\vec{b} \times \vec{a}}{[\vec{a} \, \vec{b} \, \vec{c}]}, \] then $(\vec{i} + \vec{b}) \cdot \vec{p} + (\vec{b} + \vec{c}) \cdot \vec{q} + (\vec{c} + \vec{a}) \cdot \vec{r}$ is: