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Let a=hati+hatj+hatk, b=hati-hatj+2hatk ...

Let `a=hati+hatj+hatk, b=hati-hatj+2hatk and c=x hati+(x-2) hatj-hatk`. If the vector c lies in the plane of a and b, then x equal to

A

0

B

1

C

`-4`

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
D
Since, given vectors a, b and c are coplanar.
`:. |{:(1,1,1),(1,-1,2),(x,x-2,-1):}| = 0`
`rArr 1{1-2(x-2)} -1(-1-2x)+ 1(x-2 +x) = 0`
`rArr 1 -2x + 4 + 1 + 2x + 2x- 2 = 0`
`rArr 2x = - 4`
`x = - 2`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-VECTORS -(VECTORS ) Exercise 2 ( Topical problems )
  1. Let a, b and c be three non-zero vectors which are pairwise non-collin...

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  2. Let a=hatj-hatk and c=hati-hatj-hatk, the vector b satisfying axxb+c=v...

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  3. If the vectors a=hati-hatj+2hatk, b=2hati+4hatj+hatk and c=lambdahati+...

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  4. Let a=hati+hatj+hatk, b=hati-hatj+2hatk and c=x hati+(x-2) hatj-hatk. ...

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

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  6. For any vector a, then the value of (axxhati)^(2)+(a xxhatj)^(2)+(a...

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  7. If a=hati-hatk, b=xhati+hatj=(1-x)hatk and c=yhati+xhatj+(1+x-y)hatk. ...

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

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  9. If a, b, c are non-coplanar vectors and lambda is a real number, then ...

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  10. Let a, b and c be three non-zero vectors such that no two of these are...

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  11. A particle is acted upon by constant forces 4hati+hatj-3hatk and 3hati...

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  12. Let u, v and w be such that |u|=1, |v|=2, |w|=3 If the projection ...

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  13. The value of [(a-b)(b-c)(c-a)] is equal to

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

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

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  16. Let a=hat(i)+hat(j)+hat(k), b=hat(i)-hat(j)+hat(k) and c=hat(i)-hat(j)...

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  17. If r a=r. b=r. c=1 where a, b, c are any three non-coplanar vectors, t...

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  18. If |a|=3 and -1 le k le 2, then |k a|lies in the interval

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  19. If ABCDEF is regular hexagon, then AD+EB+FC is equal to

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  20. If a=hat(i)+hat(j)+hat(k), b=hat(i)+3hat(j)+5hat(k) and c=7hat(i)+9hat...

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