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If the position vectors of the points `A , B , C ,Da r e2 hat i+4 hat k ,5 hat i+3sqrt(3) hat j+4 hat k ,-2sqrt(3) hat j+ hat ka n d2 hat i+ hat k` respectively, prove that `C D` is parallel to `A Ba n dC D=2/3A Bdot`

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Verified by Experts

Correct option is (C).
Fince, we can see that `f(x_{1})=f(x_{2})` for all values of `x_{1}` and `x_{2}`.
`\Rightarrow f(x)` is one-one.
Aso, `f(x)` is onto furction as for every `x`, there is an element
...
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RD SHARMA-ALGEBRA OF VECTORS-Solved Examples And Exercises
  1. If the points (-1,1,2),(2,m ,5)a n d(3,11 ,6) are collinear, find the ...

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  2. If vec a=3 hat i-2 hat j+ka n d vec b=2 hat i-4 hat j-3k , find | vec...

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  3. If the position vectors of the points A , B , C ,Da r e2 hat i+4 hat k...

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  4. Represent graphically i. a displacement of 40 km, 30^0 west of south ...

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  5. Classify the following measures as scalars and vectors a.10 kg b.10 m...

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  6. Classify the following measures as scalars and vectors a.30 km / hr b...

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  7. In a fig 23.4 (a square), identify the following vectors: i.Coinitial ...

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  8. In fig 23.3, which of the vectors are: i.Collinear          ii. Equal ...

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  9. Represent the following graphically: i.A displacement of 40 km, 30^0 ...

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  10. Classify the following measures as scalars and vectors: a.15 kg b. 520...

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  11. Classify the following as scalars and vector quantities: a.Time period...

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  12. In Fig. A B C D is a regular hexagon, which vectors are: Collinear ...

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  13. Answer the following as true or flase: vec a and vec b are collin...

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  14. If vec a ,\ vec b ,\ vec c be the vectors represented by the sides ...

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  15. If P ,Q and R are three collinear points such that vec P Q= vec a ...

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  16. Give a condition that three vectors vec a , vec b and vec c from ...

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  17. If vec a and vec b are two non-collinear vectors having the same ...

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  18. If vec a is a vector and m is a scalar such that m vec a= vec0 ...

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  19. If vec a , vec b are two vectors, then write the truth value of th...

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  20. If vec a , vec b are two vectors, then write the truth value of th...

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