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Find the Shortest Distance Between the Lines Whose Vector Equations Are Vecr = (Hati + 2hatj + 3hatk) + Lambda(Hati - 3hatj + 2hatk) and Vecr = 4hati + 5hatj + 6hatk + Mu(2hati + 3hatj + Hatk) - CBSE (Science) Class 12 - Mathematics

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Question

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

Solution

The given lines are   `vecr = (hati + 2hatj + 3hatk) + lambda(hati - 3hatj + 2hatk)` and `vecr = 4hati + 5hatj + 6hatk + mu(2hati + 3hatj + hatk)`

It is known that the shortest distance between the lines, `vecr = veca_1 + lambdavecb_1` and ,`vecr = veca_2 + muvecb_2` is given by,

Therefore, the shortest distance between the two given lines is `3/sqrt19` units

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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 11: Three Dimensional Geometry
Q: 16 | Page no. 478
Solution Find the Shortest Distance Between the Lines Whose Vector Equations Are Vecr = (Hati + 2hatj + 3hatk) + Lambda(Hati - 3hatj + 2hatk) and Vecr = 4hati + 5hatj + 6hatk + Mu(2hati + 3hatj + Hatk) Concept: Shortest Distance Between Two Lines.
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