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Sholve the simultasneous vector equation...

Sholve the simultasneous vector equations for `vecx aedn vecy: vecx+veccxxvecy=veca and vecy+veccxxvecx=vecb, vec!=0

Text Solution

Verified by Experts

The correct Answer is:
`vecx=(veca+vecbxxvec c+(vec c.veca)vec c)/(1+c^(2))`
`vecy=(vecb+vecaxxvec c+(vec c.vecb)vec c)/(1+c^(2))`
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Sholve the simultasneous vector equations for vecx and vecy: , vecx+veccxxvecy=veca and vecy+veccxxvecx=vecb, vec!=0

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Knowledge Check

  • Let veca, vecb, vecc be 3 mutually perpendicular unit vectors. If an unknow vector vecx satisfies the equation veca xx ((vecx - vecb) xx veca) + vecb then vecx xx (( vecx - vecc ) xx vecb ) + vecc xx (( vecx - veca) xx vecc ) = vec0 is equal to

    A
    `veca + vecb + vecc`
    B
    `(veca + vecb + vecc)/(2)`
    C
    `(veca + vecb + vecc)/(3)`
    D
    `(veca + vecb + vecc)/(4)`

  • If the vector vecx satisfying vecx xx veca +(vecx .vecb) vecc=vecd be given by vecx=lambda veca+veca xx (veca xx (vecd xx vecc))/((veca.vecc)veca^2) , then theta is equal to

    A
    `(veca.vecc)/a^2`
    B
    `(veca.vecc)/b^2`
    C
    `(vecc.vecd)/c^2`
    D
    `(veca.vecx)/a^2`

  • If veca=veci+vecj+veck, veca.vecb=1 and vecaxxvecb=vecj-veck, then vecb equals

    A
    `hati`
    B
    `hati-hatj+hatk`
    C
    `2hatj-hatk`
    D
    `2hati`

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