# Vectors

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 Ã— u |

――――

| u |

(2) Two planes having equations r . n1 = λ1 and r . n2 = λ2 intersect in the line l.

Show that a = (n1 Ã— n2) Ã— (λ2 n1 - λ1 n2 )

――――――――――― is a point on l.

| n1 Ã— n2 |Â²

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).

Â© BrainMass Inc. brainmass.com December 24, 2021, 4:53 pm ad1c9bdddfhttps://brainmass.com/math/vector-calculus/vectors-13818

#### Solution Summary

This shows how to show the shortest distance from origin to a given line