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State whether the vectors hat i, hat j a...

State whether the vectors `hat i, hat j and hat k` are coplanar or non-coplanar.

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Find the angle between the vectors hat i-hat j and hat j-hat k .

Consider the set of eight vector V={a hat i+b hat j+c hat k ; a ,bc in {-1,1}}dot Three non-coplanar vectors can be chosen from V is 2^p ways. Then p is_______.

Let vec a= hat j+hat j,vec b=hat j+hat k and vec c=alpha vec a+beta vec b . If the vectors, hat i-2hat j+hat k,3 hat i+2 hat j-hat k and vec c are coplanar then alpha/beta is

Prove that the three vectors 3 hat i +hat j+ 2 hat k , hat i-hat j-hat k and hat i +5 hat j- 4 hat k are at right angle to one another.

Find λ if the vector λ (hat i+ hat j+ hat k) is a unit vector.

Find λ if the vectors vec a = hat i+3 hat j +hat k, vec b=2 hat i- hat j- hat k and vec c=λ hat j+3 hat k are coplanar.

Find a unit vector perpendicular to both the vectors hat i-2 hat j+3 hat k and hat i+2 hat j-hat k .

Find the angle between the vectors hat i + hat j-hat k and hat i-hat j+hat k .

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. If vec a = x hat i +2 hat j - z hat k and vec b= 3 hat i- y hat j+hat ...

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  2. Does |quad vec a|= |quad vec b| imply vec a= vec b?

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  3. State whether the vectors hat i, hat j and hat k are coplanar or non-c...

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  4. Integrate the following int dx/(1-secx)

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  5. What is the cosine of the angle which the vector sqrt2 hat i+ hat j +h...

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  6. Find p if the vectors 2 hat i +3 hat j + 6 hat k and p hat i+2 hat j-...

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  7. Find λ if the vector λ (hat i+ hat j+ hat k) is a unit vector.

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  8. If vec a and vec b are non-zero vectors and the angle θ between them i...

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  9. Write a vector of magnitude 9 units in the direction vector -2hat(i)+h...

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  10. If θ is the angle between two non-zero vectors vec a and vec b , then ...

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  11. If the vectors 3hat i+2 hat j+9 hat k and hat i-2p hat j+3 hat k are p...

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  12. If for any two vectors vec a and vec b, (vec a+ vec b)^2 +(vec a - vec...

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  13. Find the angle between the vectors hat i-hat j and hat j-hat k.

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  14. If vec a* vec a =0 and vec a* vec b =0, then what can be concluded abo...

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  15. If vec (PQ) =3 hat i+3 hat j+6 hat k and Q is the point (4, 5, 6), fin...

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  16. Find vec a* vec b if vec a=3 hat i+4 hat j-2 hat k and vec b=-2 hat i+...

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  17. If (vec a+ vec b)*(vec a- vec b)=0 and |vec a|=5, find |vec b|.

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  18. If (vec a)^2 =(vec b)^2, is it necessary that vec a= vec b ?

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  19. What is the angle between two unlike parallel vectors ?

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  20. If vectors vec a and vec b, are such that |vec a| =3,|vec b| =2/3 and ...

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