Porisma

A hint to get started

Drop a normal from a point and reflect through its foot

A plane passes through (1,−2,1)(1,-2,1) and (2,−1,−1)(2,-1,-1) and is parallel to the line r=(1,−1,0)+s(3,1,−2)\mathbf r=(1,-1,0)+s(3,1,-2), s∈Rs\in\mathbb R.

(i) Find the foot of the perpendicular from A(1,1,−1)A(1,1,-1) to the plane.

(ii) Hence or otherwise find the shortest distance from A to the plane.

(iii) Find the image of A reflected in the plane.

CJC · Discussion · Question 4

Find the normal first; the perpendicular foot lies both on its line through A and on the plane.

Read the worked solution