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Show that the lines vecr=(2hatj-3hatk)...

Show that the lines
`vecr=(2hatj-3hatk)+lambda(hati+2hatj+3hatk)` and
`vecr = (2hati+6hatj+3hatk)+mu(2hati+3hatj+4hatk)`
are coplanar. Also the find the equation of the plane passing through these lines.

Answer

Step by step text solution for Show that the lines vecr=(2hatj-3hatk)+lambda(hati+2hatj+3hatk) and vecr = (2hati+6hatj+3hatk)+mu(2hati+3hatj+4hatk) are coplanar. Also the find the equation of the plane passing through these lines. by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

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Show that the line vecr = (hati+hatj-hatk)+lambda(3hati-hatj) vecr = (4hati-hatk)+mu(2hati+3hatk) are coplanar. Also find the equation of plane in which these lines lie.

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

Knowledge Check

  • The lines given by vecr = (hati - hatj) +lambda(2hati +hatk) and vecr = (2hati - hatj) + mu(hati +hatj -hatk) are

    A
    parallel
    B
    perpendicular
    C
    skew
    D
    intersecting
  • The lines vecr=(2hati-3hatj+7hatk)+lamda(2hati+phatj+5hatk) and vecr=(hati+2hatj+3hatk)+mu(3hati-phatj+phatk) are perpendicular it p=

    A
    `-6,-1`
    B
    `-1,6`
    C
    `2,3`
    D
    none of these
  • The shortest distance between the lines vecr=(hati-hatj)+lamda(hati+2hatj-3hatk) and vecr=(hati-hatj+2hatk)+mu(2hati+4hatj-5hatk) is

    A
    `6`
    B
    `6/(sqrt(5))`
    C
    `3/(sqrt(5))`
    D
    `2/(sqrt(5))`
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