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Let veca =hati + hatj+ hatk, vecb = hati...

Let `veca =hati + hatj+ hatk, vecb = hati - hatj + 2hatk` and `vecc = xhati + (x-2)hatj - hatk`. If the vector `vecc` lies in the plane of `veca` and `vecb`, then x is equal to:

A

`-4`

B

`-2`

C

`0`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
B
It is given that `veca, vecb, vecc` are coplanar.
`:.'[veca vecb vecc]=0`
`implies|(1,1,1),(1,-1,2),(x,x-2,-1)|=0`
`implies (1-2x+4)-(-1-2x)+(x-2+x)=0`
`implies2x+4=0impliesx=2`
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OBJECTIVE RD SHARMA ENGLISH-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Exercise
  1. Let veca =hati + hatj+ hatk, vecb = hati - hatj + 2hatk and vecc = xha...

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  2. For non-zero vectors veca, vecb and vecc , |(veca xx vecb) .vecc| = |v...

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  3. Let veca=hati+hatj-hatk, vecb=hati-hatj+hatk and vecc be a unit vector...

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  4. If veca lies in the plane of vectors vecb and vecc, then which of the ...

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  5. The value of [(veca-vecb, vecb-vecc, vecc-veca)], where |veca|=1, |vec...

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  6. If veca , vecb , vecc are three mutually perpendicular unit ve...

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  7. If vecr.veca=vecr.vecb=vecr.vecc=0 for some non-zero vectro vecr, then...

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  8. If the vectors ahati+hatj+hatk, hati+bhatj+hatk, hati+hatj+chatk(a!=1,...

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  9. If hata, hatb, hatc are three units vectors such that hatb and hatc ar...

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  10. For any three vectors veca, vecb, vecc the vector (vecbxxvecc)xxveca e...

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  11. for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc...

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  12. For any vectors vecr the value of hatixx(vecrxxhati)+hatjxx(vecrxxha...

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  13. If the vectors veca=hati+ahatj+a^(2)hatk, vecb=hati+bhatj+b^(2)hatk, v...

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  14. Let veca,vecb,vecc be three noncolanar vectors and vecp,vecq,vecr are ...

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  15. If vecA, vecB and vecC are three non - coplanar vectors, then (vecA.ve...

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  16. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(1)hati+b(2)hatj+b(3)hatk an...

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  17. If non-zero vectors veca and vecb are perpendicular to each ot...

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  18. show that (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc) if and only if veca a...

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  19. If veca,vecb, vecc and vecp,vecq,vecr are reciprocal system of vectors...

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  20. vecaxx(vecaxx(vecaxxvecb)) equals

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  21. If veca =hati + hatj, vecb = hati - hatj + hatk and vecc is a unit vec...

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