(i)[3]
Verify, showing all required working, that each of the angles $DAB$, $DAC$ and $CAB$ is $90^\circ$.
(ii)[4]
Find the exact value of the area of the triangle $ABC$, and hence find the exact value of the volume of the pyramid.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The diagram depicts a triangular pyramid $ABCD$. It is given that $\vec{AB} = 3\mathbf{i} + \mathbf{j} + \mathbf{k}$, $\vec{AC} = \mathbf{i} - 2\mathbf{j} - \mathbf{k}$ and $\vec{AD} = \mathbf{i} + 4\mathbf{j} - 7\mathbf{k}$.