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


    (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).

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    Solution Summary

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