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The angle between the lines r = (2hati +...

The angle between the lines `r = (2hati + hatj - 3hatk) + lambda(hati - hatj + hatk), (x-1)/1 = (y+2)/3 = (z+3)/2` is

A

`pi/6`

B

`pi/4`

C

`pi/3`

D

`pi/2`

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Verified by Experts

The correct Answer is:
D
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Find the shortest distance between the lines vecr = 2hati - hatj + hatk + lambda(3hati - 2hatj + 5hatk), vecr = 3hati + 2hatj - 4hatk + mu(4hati - hatj + 3hatk)

Find the vector and catesian equations of the plane containing the lines : vec(r) = 2 hati + hatj - 3 hatk + lambda (hati + 2 hatj + 5 hatk ) and vec(r) = 3 hati + 3 hatj - 7 hatk + mu (3 hati - 2 hatj + 5 hatk ) .

Find the shortest distance between the lines: (i) vec(r) = 6 hat(i) + 2 hat(j) + 2 hatk + lambda (hati - 2hatj + 2 hatk) and vec(r) = - 4 hati - hatk + mu (3 hati - 2 hatj - 2 hatk ) (ii) vec(r) = (4 hat(i) - hat(j)) + lambda (hati + 2hatj - 3 hatk) and vec(r) = (hati - hatj + 2hatk) + mu (2 hati + 4 hatj - 5 hatk ) (iii) vec(r) = (hati + 2 hatj - 4 hatk) + lambda (2 hati + 3 hatj + 6 hatk ) and vec(r) = (3 hati + 3 hatj + 5 hatk) + mu (-2 hati + 3 hatj + 6 hatk )

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