Consider the pair of lines whose equations are (x-2)/2 = (y-1)/5 = (z+3)/-3

Question

Consider the pair of lines whose equations are

1. Write the direction ratios of the lines. 
2. Find the shortest distance between the above skew lines. 
3. Find the angle between these two lines. 

Answer 1

1. The direction ratios are 2, 5, – 3 and – 1, 8, 4.

2. The given lines are \(\bar r\) = (2i + j – 3k) + λ(2i + 5j – 3k)

i.e. \(\bar r\) = \(\bar a_1\)+λ\(\bar b_1\),

where \(\bar a_1\) = 2i + j – 3k) + λ(2i + 5j – 3k)

and \(\bar r\)=(-i + 4j + 5k) + µ(-i + 8j + 4k)

3. cosθ