P is a point on a straight line with position vector r = a + tb. Show
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P is a point on a straight line with position vector r = a + tb. Show that
By completing the square, show that r2 is a minimum for the point P for which t = –a · b/b2. Show that at this point OP(vector) is perpendicular to the line r = a + tb. (This proves the well-known result that the shortest distance from a point to a line is the length of the perpendicular from that point to the line.)
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12atb atb a2ta bfb ab 01 120 a 2 ab b ...View the full answer
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