Home
Class 12
MATHS
Find the shortest distance between lines...

Find the shortest distance between lines:
` vec(r) = 6 hati + 2 hatj + 2 hatk + lambda ( hati - 2 hatj + 2 hatk) and`
`vec(r) = -4 hati - hatk + mu (3 hati - 2 hatj - 2 hatk)`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise REVISION EXERCISE|19 Videos
  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise CHECK YOUR UNDERSTANDING|10 Videos
  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise NCERT-FILE (EXERCISE 11.3)|14 Videos
  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (1)|12 Videos
  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise CHAPTER TEST 10|12 Videos

Similar Questions

Explore conceptually related problems

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 )

Find the shortest distance betwee the lines : vec(r) = (hati + 2 hatj + hatk ) + lambda ( hati - hatj + hatk) and vec(r) = 2 hati - hatj - hakt + mu (2 hati + hatj + 2 hatk) .

Find the shortest distance between the lines: (i) vec(r) = 3 hati + 8 hat(j) + 3 hatk + lambda (3 hati - hatj + hatk) and vec(r) = - 3 hat(i) - 7 hatj + 6 hatk + mu (-3 hati + 2 hatj + 4 hatk ) (ii) ( hati - hatj + 2 hatk) + lambda ( -2 hati + hatj + 3 hatk ) and (2 hati + 3 hatj - hatk) + mu (3 hati - 2 hatj + 2 hatk). (iii) vec(r) = (hati + 2 hatj + 3 hatk) + lambda ( hati - 3 hatj + 2 hatk ) and vec(r) = (4 hati + 5 hatj + 6 hatk) + mu (2 hati + 3 hatj + hatk) .

Find the shortest distance between the lines vecr = 3 hati + 2hatj - 4 hatk + lamda ( hati +2 hatj +2 hatk ) and vecr = 5 hati - 2hatj + mu ( 3hati + 2hatj + 6 hatk) If the lines intersect find their point of intersection

The shortest distance between the lines r = ( - hati - hatj - hatk ) + lamda ( 7 hati - 6 hatj + hatk ) and r = ( 3 hati + 5 hatj + 7 hatk ) + mu ( hati - 2 hatj + hatk )

Find the shortest distance between the lines whose vector equations are : vec(r) = (hati + 2 hatj + 3 hatk ) + lambda (hati -3 hatj + 2 hatk) and vec(r) = 4 hati + 5 hatj + 6 hatk + mu (2 hati + 3 hatj + hatk) .

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 angle between the following pairs of lines : (i) vec(r) = 2 hati - 5 hatj + hatk + lambda (3 hati + 2 hatj + 6 hatk ) and vec(r) = 7 hati - 6 hatk + mu (hati + 2 hatj + 2 hatk) (ii) vec(r) = 3 hati + hatj - 2 hatk + lambda (hati - hatj - 2 hatk ) and vec(r) = 2 hati - hatj - 56 hatk + mu (3 hati - 5 hatj - 4 hatk) .

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 ) .