Part 1A Paper 4 Mathematics Examples paper 1

Find a vector normal to both the lines

$r_1 = (1,2,3) + \lambda (4,5,6)$

$r_2 = (2,3,2) + \mu (5,6,7)$

(i) Hence find the shortest distance between the two lines. Check that your answer seems reasonable by plotting the lines with Matplotlib.

Hint: You will need to import and use a module from mpl_toolkits, e.g.

from mpl_toolkits.mplot3d import Axes3D

(ii) Calculate the shortest distance between the two lines with Python and find the points where the two lines are closest together.

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