The angle between two straight lines is α. One line has direction cosines 12,12,12 and the other line has direction ratios 0,1,2. Then tanα=

If θ is the acute angle between two lines having direction ratios a1,b1,c1and a2,b2,c2 thencosθ=a1a2+b1b2+c1c2a12+b12+c12⋅a22+b22+c22 Given α is angle between two lines having direction ratios 12,12,12 and0,1,2Hence,cosα=120+121+1221⋅02+12+22=325Use right angled triangle, to get the value of tanαTherefore,tanα=113