Miscellaneous Exercise on Chapter 11
1 Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the
line determined by the points (3, 5, – 1), (4, 3, – 1) 2 If l1, m 1, n1 and l2, m 2, n2 are the direction cosines of two mutually perpendicular
lines, show that the direction cosines of the line perpendicular to both of these
are  
1
2
2
1
1
2
2
1
1
2
2
1
,
,
m n
m n
n l
n l
l m
l m
−
−
−
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 MATHEMATI CS
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