List of top Mathematics Questions on Vector Algebra

Find the volume of the tetrahedron whose vertices are $A(3,7,4)$, $B(5, - 2, 3)$, $C(- 4, 5, 6)$ and $D(1, 2,3)$.

Area of the parallelogram whose diagonals are $\overrightarrow{a}$ and $\overrightarrow{b}$ is

A body weighing $13\, kg$ is suspended by two strings 5 m and $12 \,m$ long, their other ends being fastened to the extremities of a rod $13\, m$ long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are

Let $ABCD$ be a parallelogram such that $\overrightarrow{AB} = \vec{q}, \overrightarrow{AD} = \vec{p}$ and $?BAD$ be an acute angle. If $\vec{r}$ is the vector that coincides with the altitude directed from the vertex $B$ to the side $AD$, then $\vec{r}$ is given by :