Find the angle between two lines whose direction ratios are
i. 2, 1, 2 and 4, 8, 1
ii. 5, -12, 13 and -3, 4, 5
iii. 1, 1, 2 and 
iv. a, b, c and (b – c), (c – a), (a – b)
(i): Given – Direction ratios of L1 = (2,1,2) & Direction ratios of L2 = (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 L1 = (5,-12,13) & Direction ratios of L2 = (-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 L1 = (1,1,2) & Direction ratios of L2 = (√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 L1 = (a,b,c) & Direction ratios of L2 = ((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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