Problems:
Vector Problems:
(1) Let l be the line with equation v = a + t u.
Show that the shortest distance from the origin to l can be written |a×u|/|u|
(2) Two planes having equations r . n1 = λ1 and r . n2 = λ2 intersect in the line l.
Show that a = (n1 × n2) × (λ2 n1 - λ1 n2 )/| n1 × n2 |² is a point on1.
Hence find the point where the three planes
r . n1 = λ1 , r . n2 = λ2 , r . n3 = λ3 .
(Assume that the planes do intersect in a point).