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Lines vecr = veca(1) + lambda vecb(1) an...

Lines `vecr = veca_(1) + lambda vecb_(1) and vecr = veca_(2) + svecb_(2)` will lie in a Plane if

A

`|((vecb_(1)xx vecb_(2))xx(veca_(2)-veca_(1)))/(vecb_(1)xx vecb_(2))|`

B

`|((veca_(2)xx veca_(1))xx(vecb_(2)-vecb_(1)))/(vecb_(1)xx vecb_(2))|`

C

`|((veca_(2)xx veca_(1)).(vecb_(2)-vecb_(1)))/(vecb_(1)xx vecb_(2))|`

D

`|((veca_(2)xx veca_(1)).(vecb_(2)-vecb_(1)))/(vecb_(1)xx vecb_(2))|`

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • Lines vecr = veca _(1)+veca _(2)and vecr = veca _(2)+ vecb _(2) lie in a plane if :

    A
    `vecb _(1) xx vecb _(2)=0`
    B
    ` (veca _(1) - veca_(1)) (vecb _(1) xx vecb _(2)) =0`
    C
    `veca _(1) xx veca _(2) =0`
    D
    None of these

  • The lies vecr=veca_(1)+lamdavecb_(1) and vecr-veca_(2)+muvecb_(2) are coplanar if

    A
    `veca_(1)xxveca_(2)=vec0`
    B
    `vecb_(1)xxvecb_(2)=0`
    C
    `(veca_(2)-veca_(1))xx(vecb_(1)xxvecb_(2))=0`
    D
    `[(veca_(1),vecb_(1),vecb_(1))]=[(veca_(2),vecb_(2),vecb_(2))]`

  • Lines vecr xx vecb = veca xx vecb and vecr xx veca = vecb xx veca , where veca =hati + hatj, vecb = 2hati -hatk intersect at

    A
    `3hati - hatj - hatk`
    B
    `3hati + hatj - hatk`
    C
    `3hati -hatj +hatk`
    D
    `3hati + hatj + hatk`

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