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

The value of `[a-b b-c c-a]` is equal to

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
`[(a-b,b-c,c-a)]`
`={(a-b)xx(b-c)}.(c-a)`
`=(axxb-axxc-bxxb+bxxc).(c-a)`
`=(axxb+cxxa+bxxc).(c-a)`
`=(axxb).c-(bxxc).a`
`=[abc]-[abc]=0`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-VECTORS -( MHT CET Corner)
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  2. If a=hat(i)+hat(j)-2hat(k), b=2hat(i)-hat(j)+hat(k) and c=3hat(i)-hat(...

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  3. If M and N are the mid-points of the diagonals AC and BD respectively ...

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  4. If G(barg), H(barh) and P(barp) are centroid, orthocenter and circumce...

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  5. If a=hat(i)+hat(j)+hat(k), b=2hat(i)+lambda hat(j)+hat(k), c=hat(i)-ha...

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  6. If the position vectors of the vertices A, B and C are 6i, 6j ...

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  7. If three vectors 2hat(i)-hat(j)-hat(k), hat(i)+2hat(j)-3hat(k) and 3ha...

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  8. Find a vector of magnitude 9, which is perpendicular to both vectors 4...

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  9. If in a Delta ABC, O and O' are the incentre and orthocentre respectiv...

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  10. If a+b+c=0 and |a|=5, |b|=3 and |c|=7, then angle between a and b is

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  11. If vecu=veca-vecb,vecv=veca+vecb and |veca|=|vecb|=2, then |vecuxxvecv...

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  12. If a, b, c are linearly independent vectors and delta =|(a,b,c),(a.a,a...

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  13. If veca,vecb,vecc are three non- coplanar vectors and vecp,vecq,vecr a...

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  14. The volume of a parallelopiped whose coterminous edges are 2veca , 2ve...

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  15. The position vectors of vertices of a Delta ABC are 4hat(i)-2hat(j), h...

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  16. Given p=3hat(i)+2hat(j)+4hat(k), a=hat(i)+hat(j), b=hat(j)+hat(k), c=h...

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  17. Volume of the parallelopiped having vertices at O-=(0,0,0) , A-=(2,-2...

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  18. If 2veca+ 3vecb-5 vecc=vec0, then ratio in which vecc divides vec...

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  19. If the constant forces 2hati-5hatj+6hatk and -hati+2hatj-hatk act on a...

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  20. If the vectors hat(i)-3hat(j)+2hat(k), -hat(i)+2hat(j) represent the d...

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  21. If |vec(a)|=2,|vec(b)|=3andvec(a),vec(b) are mutually perpendicular, t...

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