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

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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).