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Find the shortest distance between the lines `l_1` and `l_2` `barr=hati+hatj+ lambda(2 hati-hatj+k)` and
`barr=2 hati+hatj-hatk+mu^*(3 hati-5hatj+2 hatk)`

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Find the distance between the lines l_1 and l_2 , given by barr=hati+2 hatj-4 hat k+lambda(2 hati+3 hatj+6 hatk) and barr=3 hati+3 hatj-5 hatk+mu(2 hati+dot3 hatj+6 hatk)

Find the shortest distance between the lines: vecr=3 hati+8 hatj+3 hatk+lambda(3 hati-hatj+hatk) and vecr=-3 hati-7 hatj+6 hatk+mu(-3 hati+2 hatj+4 hatk)

Knowledge Check

  • The angle between the lines vecr = hati + 4hatk+ lambda ( 2 hati + hatj - hatk) and vecr =2hati -hatj +3hatk + mu( 3hati + hatk) is

    A
    `cos^(-1) ((sqrt(5))/(6))`
    B
    `cos^(-1) ((sqrt(15))/(6))`
    C
    `cos^(-1)((1)/(12))`
    D
    `cos^(-1)((sqrt(15))/(15))`

  • The distance between the line vecr=2hati-2hatj+3hatk+lambda(hati-hatj+4hatk) and the plane vecr*(hati +5hatj+hatk)=5 is

    A
    `(10)/(3sqrt(3))`
    B
    `(10)/(9)`
    C
    `(10)/(3)`
    D
    `(3)/(10)`

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    Explore conceptually related problems

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

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

    Find the shortest distance between the lines vecr = 6hati+2hatj+2hatk+lambda(hati-2hatj+2hatk) and vecr = -4hati-hatk+mu(3hati-2hatj-2hatk)

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

    Find the angle between the pair of lines given by barr=3 hati+2 hatj-4 hatk+lambda(hati+2 hatj+2 hatk) and vecr=5 hati -2 hatj+mu(3 hati+2 hatj+6 hatk)

    Find the angle between the line vecr=hati +2hatj -hatk +lambda(hati-hatj+hatk) and the plane vecr*(2hati-hatj+hatk)=4 .

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