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Let vec a=2 hat i- hat j+ hat k , vec b...

Let ` vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j= hat ka n d vec c= hat i+ hat j-2 hat k` be three vectors. A vector in the plane of ` vec ba n d vec c` , whose projection on ` vec a` is of magnitude `sqrt(2//3)` , is `2 hat i+3 hat j-3 hat k` b. `2 hat i-3 hat j+3 hat k` c. `-2 hat i- hat j+5 hat k` d. `2 hat i+ hat j+5 hat k`

A

`2i+3j-3k`

B

`2i+3j+3k`

C

`-2i-j+5k`

D

`2i+j+5k`

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The correct Answer is:
A, C
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ML KHANNA-ADDITION AND MULTIPLICATION OF VECTORS -Self Assessment Test (MULTIPLE CHOICE QUESTIONS)
  1. The volume of a parallelopiped whose sides are given by vecOA =2i-3j,v...

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  2. If alpha = 2i + 3j - k, beta = -i + 2j-4k, gamma = i+j+k then the valu...

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  3. Let vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j= hat ka n d ve...

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  4. If the vectors vec c , vec a=x hat i+y hat j+z hat ka n d vec b= hat ...

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  5. If veca lies in the plane of vectors vecb and vecc, then which of the ...

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  6. If a xx b = c, b xx c = a and a, b,c be moduli of the vectors a, b,c...

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  7. Let a-i+j and b=2i-k.The point of intersection of the lines r times a=...

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  8. Let a,b, c be three non-coplanar vectors and r be any vector in space ...

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  9. Let a, b, c be unit vectors such that a + b + c = 0 which one of the f...

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  10. Unit vector vecc is inclined at an angle theta to unit vectors ve...

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  11. If hata,hatb,hatc and hatd are unit vectors such that (hata xx hatb). ...

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  12. If vecu, vecv, vecw are non -coplanar vectors and p,q, are real numbe...

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  13. Let ABCD be a parallelogram such that vec A B= vec q , vec A D= vec p...

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  14. Two vectors a and b are not perpendicular and c and d are two vectors ...

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  15. IF a and b are vectors such that | a + b| = sqrt(29) and a xx (2i+3j+4...

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  16. If the vectors a = i-j+2k, b =2i+4j+k and c=lambdai+j+mu k are mutuall...

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  17. Let P ,Q ,R and S be the points on the plane with position vectors ...

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  18. If a=1/sqrt(10)(3i+k)" and "b=1/7(2i+3j-6k), then the value of (2a-b)....

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  19. Two adjacent sides of a parallelogram ABCD are given by vec(AB)=2hati+...

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  20. The vector(s) which is/are coplanar with vectors hat(i)+hat(j)+2hat(k)...

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