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Find the vector of length 3 unit whic...

Find the vector of length 3 unit which is perpendicular to ` hat i+ hat j+ hat k` and lies in the plane of ` hat i+ hat j+ hat ka n d2 hat k-3 hat j` .

A

`(3)/(sqrt(6))(hat(i) - 2hat(j) + hat(k))`

B

`(3)/(sqrt(6))(2hat(i) - hat(j) - hat(k))`

C

`(3)/(sqrt(114)) (8hat(i) - 7hat(j) -hat(k))`

D

`(3)/(sqrt(114))(-7hat(i) + 8hat(j) - hat(k)) `

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The correct Answer is:
D
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MOTION-VECTOR -EXERCISE - 1
  1. Unit vector perpendicular to the plane of DeltaABC with position vecto...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Consider the vectors, vec(a),vec(b),vec(c),vec(d) such that (vec(a)xxv...

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  17. If veca,vecb,vecc are linearly independent vectors, then which one of ...

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  18. A point taken on each median of a triangle divides the median in the r...

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  19. If G is the centroid of triangle A B C ,t h e n vec G A+ vec G B+ vec ...

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  20. The vector bar(AB)=3hati+4hatk and bar(AC)=5hati-2hatj+4hatk are the s...

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