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Question

If l1,m1,n1 and l2,m2,n2 are the direction cosines of two perpendicular lines, then the direction cosine of the line which is perpendicular to both the lines, will be
  1. (l1l2m1m2),(m1m2n1n2),(n1n2l1l2)
  2. 1l21+m21+n21,1l22+m22+n22,13
  3. 13,13,13
  4. (m1n2m2n1),(n1l2n2l1),(l1m2l2m1)
     


Solution

The correct option is D (m1n2m2n1),(n1l2n2l1),(l1m2l2m1)
 
Let lines are l1x+m1y+n1z+d=0...(i)
and l2x+m2y+n2z+d=0...(ii)
If lx+my+nz +d =0 is perpendicular to (i) and (ii), then ,ll1+mm1+nn1=0,ll2+mm2+nn2=0
lm1n2m2n1=mn1l2l1n2=nl1m2l2m1=d
Therefore, direction cosines are
(m1n2m2n1),(n1l2l1n2),(l1m2l2m1).
 

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