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Home  >>  CBSE XII  >>  Math  >>  Three Dimensional Geometry
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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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1 Answer

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Toolbox:
  • Solve the two equations to get the d.r of both the lines $ d_1, d_2$
  • Prove $ d_1.d_2=0$ for right angle.
Step 1
$ 2l+2m=n$ ...............(1) put n in
$ mn+nl+lm=0$......(2)
Step 2
$ 2lm+2m^2+2l^2+2lm+lm=0$
Step 3
$ 2m^2+5lm+2l^2=0 $
Step 4
factorise and get
$ (m+2l)(2m+l)=0$
$ \Rightarrow m= -2l\: or \: m=\large\frac{-l}{2}$
Step 5
Put $ l=1\: then \: d_1=(1, -2, -2)\: and \: d_2 ( 1, \large\frac{-1}{2}, 1)$
Step 6
$ d_1.d_2=0$

 

answered Mar 7, 2013 by thanvigandhi_1
edited Apr 5, 2013 by thanvigandhi_1
 

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