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Find the shortest distance between the following pair of line: `vecr=hati+2hatj+hatk+lamd(hati-hatj+hatk) and vecr=2hati-hatj-hatk+mu(2hati+hatj+2hatk)`

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The correct Answer is:
`(1) (3)/(sqrt(2))` units (2) `(1)/(sqrt(5))` units
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Find the shortest distance between the following pair of line: vecr=hati+2hatj+hatk+lamda(hati-hatj+hatk) and vecr=2hati-hatj-hatk+mu(2hati+hatj+2hatk)

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Find the shortest distance between the following pair of line: vecr=hati+hatj+lamda(2hati-hatj+2hatk), vecr=2hati+hatj-hatk+mu(3hati-5hatj+2hatk)

Find the angle between the following pair of line: vecr=3hati+hatj-2hatk+lamda(hati-hatj-2hatk) and vecr=2hati-hatj-56hatk+mu(3hati-5hatj-3hatk)

Find the shortest distance between the following lines : (i) vecr=4hati-hatj+lambda(hati+2hatj-3hatk) and vecr=hati-hatj+2hatk+mu(2hati+4hatj-5hatk) (ii) vecr=-hati+hatj-hatk+lambda(hati+hatj-hatk) and vecr=hati-hatj+2hatk+mu(-hati+2hatj+hatk) (iii) (x-1)/(-1) = (y+2)/(1) = (z-3)/(-2) and (x-1)/(1) = (y+1)/(2) = (z+1)/(-2) (iv) (x-1)/(2) = (y-2)/(3) = (z-3)/(4) and (x-2)/(3) = (y-3)/(4) = (z-5)/(5) (v) vecr = veci+2hatj+3hatk+lambda(hati-hatj+hatk) and vecr = 2hati-hatj-hatk+mu(-hati+hatj-hatk)

Find the shortest distance between the lines vecr=(hati+2hatj+hatk)+lamda(2hati+hatj+2hatk) and vecr=2hati-hatj-hatk+mu(2hati+hatj+2hatk) .

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

Find the angle between the pair of line: vecr=4hati=hatj+lamda(hati=2hatj-2hatk) and vecr=hati-hatj+2hatk-mu(2hati+3hatj-4hatk)

If d is the shortest distance between the lines vecr =(3hati +5hatj + 7hatk)+lambda (hati +2hatj +hatk) and vecr = (-hati -hatj-hatk)+mu(7hati-6hatj+hatk) then 125d^(2) is equal to ____________.

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