Question

The angle between the lines whose direction cosines satisfy the equation

Answer 1

Step 1:Given that l+m+n=0 -----(1)=>l+m=−n=>−(l+m)=nand l2+m2−n2=0-----(2)Let us substitute for ′n′ in equation (2) we get=>l2+m2−l2−m2−2ml=0or 2ml=0(ie) either l=0orm=0Let us put m=0 in equation (1)If m=0 then l=−ndirection ratios (l,m,n)=(1,0,−1)Let us put l=0 we get m=−ndirection ratios (l,m,n)=(0,1,−1)Step 2:Let us find out b1.b2b1.b2=(1,0,−1).(0,1,−1)=0+0+11|b1|=02+12+(−1)2−−−−−−−−−−−−−√=2–√|b2|=02+12+(−1)2−−−−−−−−−−−−−√=2–√Step 3:Now substituting the above values incosθ=b1→.b2→|b1→||b2→|cosθ=12–√2–√=12=>θ=π3answered Jun 11, 2013 by meena.p