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If vec(p)=hat(i)+hat(j), vec(q)=4hat(k)-...

If `vec(p)=hat(i)+hat(j), vec(q)=4hat(k)-hat(j)` and `vec(r )=hat(i)+hat(k)` then the unit vector in the direction of `3vec(p)+vec(q)-2vec(r )` is

A

i+2j+2k

B

1/3 (i-2j+2k)

C

1/3 (i-2j-2k)

D

1/3 (i+2j+2k)

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The correct Answer is:
D
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HIMALAYA PUBLICATION-VECTORS AND THEIR APPLICATIONS-QUESTION BANK
  1. If vec a, vec b, vec c are three vectors such that vec a . (vec b + ve...

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  2. If the area of the parallelogram with vec(a) and vec(b) as two adjacen...

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  3. If vec(p)=hat(i)+hat(j), vec(q)=4hat(k)-hat(j) and vec(r )=hat(i)+hat...

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  4. If vec(a) and vec(b) are the vectors such that |vec(a)|=3sqrt(3), |vec...

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  5. If vec(a) is vector perpendicular to both vec(b) and vec(c ), then

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  6. A vector perpendicular to the plane contianing the points A(1,-1,2), B...

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  7. vec OA and vec BO are two vectors of magnitudes 5 and 6 respectively.I...

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  8. If veca = 2 hat i + 3 hat j - hat k , vec b = hat i + 2 hat j - 5 hat ...

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  9. The projection of a = 3i - j + 5k on b = 2i + 3j +k is

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  10. The area of the triangle whose vertices are A = (1,-1,2), B= (2,1,-1) ...

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  11. The volume of a parallelopiped whose adjacent sides are vec a = i+2j, ...

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  12. If ai+j+k, i+bj+k and i+j+ck are coplanar, then

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  13. If A, B, C and D aare four points and vec AB = vec DC then vec AC + ve...

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  14. The value of [vec a - vec b, vec b - vec c , vec c - vec a] where |...

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  15. If the veactors veca, vecb and vecc form the sides BC,CA and AB respec...

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  16. If vec a = 3i-5j and vec b = 6i+3j are two vectors vec c a vector such...

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  17. Given two vectors hati + hatj and hati +2 hatj, the unit vector coplan...

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  18. If the vectors vec c , veca = x hati + y hatj + z hatk and vecb = hatj...

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  19. The vector hati + hatj + 3 hatk is rotated through an angle theta and...

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  20. If vec u, vec nu, vec w are three non-coplanar vectors, then (vec u + ...

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