Question 1318

Vectors II: Lines and Planes

2018 Paper 2 Question 3 Variant

Question

An oblique pyramid has a plane base

{ABCD}

in the shape of a parallelogram. The coordinates of

{A, B}

and

{C}

are

{\left( 3, 2, 2 \right), }

{\left( - 3, 2, 0 \right)}

and

{\left( 3, - 2, 1 \right)}

respectively. The apex of the pyramid is at

{E \left( 0, 0, 8 \right).}

(i)

Find the coordinates of

{D.}

[1]

(ii)

Find the cartesian equation of face

{BCE.}

[3]

(iii)

Find the angle between face

{BCE}

and the base of the pyramid.

[3]

(iv)

Find the shortest distance from the midpoint of edge

{AD}

to face

{BCE.}

[5]