Find the product. (2l+ m)(l-2m+n)
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12th
Maths
Three Dimensional Geometry
Angles between Two lines in 3D Space
Show that the straight line...
MATHS
Show that the straight lines whose direction cosines are given by 2l+2m−n=0 and mn+nl+lm=0 are at right angles.
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2l+2m=n ...............(1)
put n in mn+nl+lm=0......(2)
⇒2lm+2m
2
+2l
2
+2lm+lm=0
⇒2m
2
+5lm+2l
2
=0
⇒2m
2
+4lm+lm+2l
2
=0
⇒2m(m+2l)+l(m+2l)=0
⇒(m+2l)(2m+l)=0
⇒m=−2l,m=
2
−l
Put l=1⇒d
1
=(1,−2,−2) and d
2
=(1,
2
−1
,1)
⇒d
1
d
2
=0
Hence the given lines are at right angles.
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