Let L be the line of intersection of the planes  2x+3y+z=1 andx+3y+2z=2. If L makes an angle α with the positive x-axis, then cos αequals

[c] Let the direction cosines of line L be l, m, n, then 2l+3m+n=0                        (i) And l+3m+2n=0                   (ii) On solving equations (i) and (ii), we get l6−3=m1−4=n6−3⇒l3=m−3=n3 Now l3=m−3=n3=l2+m2+n2−−−−−−−−−−√32+(−3)2+32−−−−−−−−−−−−−√ ∴l2+m2+n2=1∴l3=m−3=n3=127−−√ ⇒l=327−−√=13√,m=−13√,n=13√ Line L, makes an angle α with +vex−axis ∴l=cosα⇒cosα=13√