1. Mathematics
2. Geometry and Topology
3. Analytic Geometry
4. Vector Calculus
5. 13818

Please see attachment. Require problems solving, also explanations etc for better understanding of vectors.

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 )
――――――――――― is a point on l.
| n1 × n2 |²

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).

Attachments

• VECTOR PROBLEMS.doc