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Let veca=hatj-hatk and vecc=hati-hatj-ha...

Let `veca=hatj-hatk` and `vecc=hati-hatj-hatk`. Then the vector `vecb` satisfying `vecaxxvecb+vecc=vec0` and `veca.vecb=3` is

A

`-hati+hatj-2hatk`

B

`2hati-hatj+2hatk`

C

`hati-hatj-2hatk`

D

`hati+hatj-2hati`

Text Solution

Verified by Experts

The correct Answer is:
A
Given , `a xx b + c = 0`
`rArr a xx (a xx b) + a xx c = 0`
`rArr (a.b)a - (a.a) + a xx c = 0`
`rArr 3a - 2b +a xx c = 0`
`rArr 2b = 3a+ a xx c`
`rArr 2b = 3hatj - 3hatk -2hati - hatj - hatk`
`rArr 2b = - hati + 2hatj - 4hatk`
`:. b = - hati + hatj - 2hatk`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-VECTORS -(VECTORS ) Exercise 2 ( Topical problems )
  1. If the vectots phati+hatj+hatk, hati+qhatj+hatk and hati+hatj+rhatk(p!...

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  2. Let a,b and c be three non-zero vectors which are pairwise non-colline...

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  3. Let veca=hatj-hatk and vecc=hati-hatj-hatk. Then the vector vecb satis...

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  4. If the vectors veca=hati-hatj+2hatk, vecb=2hati+4hatj+hatk and vecc=la...

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  5. Let veca=hati+hatj+hatk, vecb=hati-hatj+2hatk and vecc=xhati+(x-2)hatj...

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  6. The value of 'a' for which the points A, B,C with position vectors ...

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  7. For any vector veca the value of (vecaxxhati)^2+(vecaxxhatj)^2+(vecaxx...

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  8. Let veca=hati-hatk, vecb=xhati+hatj+(1-x)hatk and vecc=yhati+xhatj+(1+...

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  9. Let a,b,c be distinct non-negative numbers. If the vectors ahati+ahatj...

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  10. If bar a,bar b,bar c are non coplanar vectors and lambda is a real nu...

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  11. If a,b and c are three non-zero vectors such that no two of these are ...

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  12. A paticle acted on by constant forces 4hati=hatj-3hatk and 3hati+hatj-...

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  13. Let vec u , vec va n d vec w be such that | vec u|=1,| vec v|=2a n d|...

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  14. The value of [[a-b , b-c ,c-a]] is equal to

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  15. If hat(i)+hat(j), hat(j)+hat(k), hat(i)+hat(k) are the position vector...

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  16. If a, b and c are three non-zero vectors such that each one of them be...

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  17. Let vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec ...

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  18. If vec r.vec a=vec r.vec b=vec r.vec c=0 where a, b, c are non-coplan...

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  19. If |veca|=3 and -1 <= k <= 2, then |kveca| lies in the interval

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  20. If ABCDEF is a regular hexagon then vec(AD)+vec(EB)+vec(FC) equals :

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