1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# The straight lines whose direction cosines are given by al + bm + cn = 0, fmn + gnl + hlm = 0 are perpendicular, if

A

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A From the first relation,n=−(al+bmc) Put the value of n in second relation, fm(−(al+bm)c)+gl(−(al+bm)c)+hlm=0 or afml+bfm2+agl2+bglm−chlm=0 agl2m2+lm(af+bg−ch)+bf=0 .....(i) Now if l1,m1,n1 and l2,m2,n2 be direction cosines of two lines, then from (i) l1l2f/a=m1m2g/b=n1n2h/c=q (Say) or l1l2f/a=m1m2g/b Similarly, elimination of l will yield m1m2g/b=n1n2h/c ∴l1l2f/a=m1m2g/b=n1n2h/c=q (Say) We know that the lines are perpendicular, if l1l2+m1m2+n1n2=0 i.e.,(fa)q+(gb)+(hc)q=0 or fa+gb+hc=0. Note: Student should remember this question as a fact.

Suggest Corrections
8
Join BYJU'S Learning Program
Related Videos
Tango With Straight Lines !!
MATHEMATICS
Watch in App
Join BYJU'S Learning Program