Mathematics

Problem

A surveyor measures a plot of land defined by the vectors

\overrightarrow{AB} = 3\vec{i} + 4\vec{j}

and

\overrightarrow{AC} = 8\vec{j}

(where

\vec{i}

and

\vec{j}

are unit vectors in meters). This triangular plot is excavated vertically to a depth of

5\,\text{m}

to create a cellar. Find the volume of earth removed.