The direction cosines
, of one of the two lines connected by the relations
are
Text Solution
Verified by ExpertsA
From the first relation,
. Putting this value of
in second relation


or 
Note that it, being quadratic in
, gives two sets of values of
, and hence gives the d.r.s. of two lines.
Now, factorising it, we get
or 
either
or 
Taking
we get
.
Also putting
in
, we get

Thus, we get,
or 
d.r.'s of one line are
.
Hence, the dc's. of one line are
or 
Taking
, we get
or
.
Putting this value in
, we obtain
or 
Thus 
the d.r's of the second line are 1,2,3; and hence d.c.s. of sccond line are
or 
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