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Does |quad vec a|= |quad vec b| imply ve...

Does `|quad vec a|= |quad vec b|` imply `vec a= vec b`?

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Given |quad vec a|=10 , |quad vec b|=2 and vec a *vec b=12 , find | vec a cross vec b| .

If vec a and vec b are two vectors such that |quad vec a|=2 , |quad vec b|=1 and vec a. vec b=1 , then find the value of (3 vec a - 5 vec b).(2 vec a+7 vec b) .

If vec a and vec b are two vectors such that |quad vec a| =10 , |quad vec b|=15 and vec a.vec b=75 sqrt 2 , find the angle between vec a and vec b .

If vec a , vec b and vec c are three vectors such that vec a+vec b+vec c=vec 0 , |quad vec a|=1 , |quad vec b|=4 and |quad vec c|=2 , then find the value of vec a.vec b+vec b.vec c+vec c.vec a .

If vec a, vec b, vec c are three vectors such that |quad vec a|=5,| , quad vec b|=12 and |quad vec c|=13 and if vec a+ vec b+ vec c= 0 , find the value of vec a* vec b + vec b* vec c + vec c* vec a .

If |quad vec a+ vec b|=|quad vec a- vec b| , prove that vec a and vec b are perpendicular.

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If |quad vec a|=1 , |quad vec b|=1 and |quad vec a+ vec b|=1 , prove that | vec a- vec b|= sqrt 3 .

If vec a and vec b are two vectors such that |quad vec a + vec b|= |quad vec a| , then prove that 2 vec a+ vec b is perpendicular to the vector vec b .

If vec a , vec b and vec c are three proper vectors such that vec a * vec b=vec c , vec b*vec c=vec a . Prove that vec a , vec b , vec c are mutually at right angles and |quad vec b|=1 ,|quad vec c|=|quad vec a|.

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. What is the magnitude of a unit vector ?

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

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

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

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

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

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

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

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

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

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

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

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  16. 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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  17. 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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  18. If (vec a+ vec b)*(vec a- vec b)=0 and |vec a|=5, find |vec b|.

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

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

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