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Consider the lines barr=(hati+2hatj+3hat...

Consider the lines `barr=(hati+2hatj+3hatk)+lambda(2hati-3hatj-4hatk)` , `barr=(hati+hatj+hatk)+mu(hati+3hatj+2hatk)`
Write the Cartesian equation.

Answer

Step by step text solution for Consider the lines barr=(hati+2hatj+3hatk)+lambda(2hati-3hatj-4hatk) , barr=(hati+hatj+hatk)+mu(hati+3hatj+2hatk) Write the Cartesian equation. by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

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Explore conceptually related problems

Consider the lines barr=(hati+2hatj+3hatk)+lambda(2hati-3hatj-4hatk) , barr=(hati+hatj+hatk)+mu(hati+3hatj+2hatk) Find the angle between the lines.

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

Knowledge Check

  • The line through hati+3hatj +2hatk and perpendicular to the line vecr =(hati +2hatj -hatk) + lambda (2hati+hatj +hatk) and vecr =(2hati +6hatj +hatk) + mu(hati +2hatj +3hatk) is

    A
    `vecr=(hati +2hatj -hatk ) +lambda (-hati +5hatj -3hatk)`
    B
    `vecr =hati+3hatj +2hatk +lambda(hati-5hatj +3hatk)`
    C
    `vecr=hati +3hatj +2hatk +lambda (hati+5hatj +3hatk)`
    D
    `vecr =hati +3hatj +2hatk +lambda(-hati -5hatj -3hatk)`

  • If vecr = (hati +2hatj +3hatk)+lambda (hati-hatj +hatk) and vecr =(hati +2hatj+3hatk)+mu(hati+hatj-hatk) are two lines, then the equation of acute angle bisector of two lines is

    A
    `vecr =(hati +2hatj+3hatk)+t(hatj-hatk)`
    B
    `vecr=(hati+2hatj +3hatk) +t(2hati)`
    C
    `vecr =(hati+2hatj+3hatk)+t(hatj+hatk)`
    D
    None of these

  • 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))`

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    Explore conceptually related problems

    Consider the straight lines vecr=(hati+2hatj+hatk)+lambda(hati-hatj+hatk )and vecr=2hati-hatj-hatk+mu(2hati+hatj+2hatk ) Show that these lines are not coplanar.

    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 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)

    Consider the line vecr = (hati+2hatj-hatk)+lambda(2hati+hatj+4hatk) and the plane vecr .(hati-6hatj+hatk)+12=0 .Prove that the line lies on the plane.

    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)

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