Answer :

**(i): Given –** Direction ratios of L_{1} = (2,1,2) & Direction ratios of L_{2} = (4,8,1)

**To find –** Angle between the two pair of lines

**Tip –** If (a,b,c) be the direction ratios of the first line and (a’,b’,c’) be that of the second, then the angle between these pair of lines is given by

The angle between the lines

**(ii): Given –** Direction ratios of L_{1} = (5,-12,13) & Direction ratios of L_{2} = (-3,4,5)

**To find –** Angle between the two pair of lines

**Tip –** If (a,b,c) be the direction ratios of the first line and (a’,b’,c’) be that of the second, then the angle between these pair of lines is given by

The angle between the lines

**(iii) Given –** Direction ratios of L_{1} = (1,1,2) & Direction ratios of L_{2} = (√3-1,-√3-1,4)

**To find –** Angle between the two pair of lines

**Tip –** If (a,b,c) be the direction ratios of the first line and (a’,b’,c’) be that of the second, then the angle between these pair of lines is given by

The angle between the lines

**(iv) Given –** Direction ratios of L_{1} = (a,b,c) & Direction ratios of L_{2} = ((b-c),(c-a),(a-b))

**To find –** Angle between the two pair of lines

**Tip –** If (a,b,c) be the direction ratios of the first line and (a’,b’,c’) be that of the second, then the angle between these pair of lines is given by

The angle between the lines

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