Q. 12

# Find the angle between two lines whose direction ratios arei. 2, 1, 2 and 4, 8, 1ii. 5, -12, 13 and -3, 4, 5iii. 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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