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Let ` vec a , vec ba n d vec c` be three units vectors such that `2 vec a+4 vec b+5 vec c=0.` Then which of the following statement is true? a. ` vec a` is parallel to ` vec b` b. ` vec a` is perpendicular to ` vec b` c. ` vec a` is neither parallel nor perpendicular to ` vec b` d. none of these

A

`vec(a)` is parallel to `vec(b)`

B

`vec(a)` is perpendicular to `vec(b)`

C

`vec(a)` is neither parallel nor perdendicular to `vec(b)`

D

None of these

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The correct Answer is:
B
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MOTION-VECTOR -EXERCISE - 1
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  2. Given the three vectors vec(a) = - 2hati + hat(j) + hat(k), vec(b) = ...

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  3. Let vec a , vec ba n d vec c be three units vectors such that 2 vec a...

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  4. Let vec a = hati+hatj and vec b = 2 hat i - hat k. The point of inters...

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  5. Vectors aa n db make an angle theta=(2pi)/3dot If | vec a|=1,| vec b|=...

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  6. Unit vector perpendicular to the plane of DeltaABC with position vecto...

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  7. If vec(b) and vec(c) are two non-collinear vectors such that vec(a)...

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  8. Find the vector of length 3 unit which is perpendicular to hat i+ ...

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  9. Given the vertices A(2,3,1), B(4,1,-2), C(6,3,7) and D(-5,-4,8) of a ...

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  10. For a non zero vector vec(A) . If the equations vec(A).vec(B) = vec...

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  11. If vecu and vecv are unit vectors and theta is the acute angle bet...

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

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  13. If A(1,1,1),C(2,-1,2) the vector equation of the line vec(AB) is v...

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  14. The value of [(veca -2vecb-vecc)(veca-vecb)( veca-vecb-vecc)] is equal...

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  15. The volume of the parallelopiped constructed on the diagonals of the f...

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  16. If vec u , vec va n d vec w are three non-cop0lanar vectors, then ...

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  17. Let overset(to)(a) =a(1) hat(i) + a(2) hat(j) + a(3) hat(k) , overse...

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  18. Vector vec x satisfying the relation vec A . vec x = c and vec B xx v...

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  19. If vec a , vec b ,a n d vec c be non-zero vectors such that no tow...

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  20. The pairs vec a,vec b and vec c,vec d each determines plane. Then the ...

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