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Show that the vectors vec a= 10 hat i -1...

Show that the vectors `vec a= 10 hat i -12 hat j -4 hat k, vec b=-16 hat i +22 hat j- 2 hat k and vec c = 2hat i -8 hat j +16hat k` are coplanar.

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Find λ such that 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 i +7 hat j +3 hat k are coplanar.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. If vec α and vec β are any vectors, prove that vec β * (vec α xx vec β...

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  2. If vec a = -2hat i -2 hat j + 4 hat k, vec b=-2 hat i +4 hat j- 2 hat...

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  3. Show that the vectors vec a= 10 hat i -12 hat j -4 hat k, vec b=-16 ha...

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  4. If vec a = hat i +2 hat j +hat k, vec b= 3 hat i +2 hat j- 7hat k and ...

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  5. Integrate the following int xe^(3x)dx

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  6. Find λ if vectors vec a = hat i +λ hat j +hat k, vec b= 2hat i -hat ...

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  7. Find the value of scalar λ if the vectors vec a =2 hat i +hat j +hat ...

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  8. Prove that the four points 4 hat i +5 hat j +hat k, -(hat j+hat k) ,3...

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  9. Integrate the following int (2x+6)dx/(x^2+6x+49)

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  10. Show that the four points having position vectors 6 hat i-7 hat j, 16 ...

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  11. Integrate the following int xlog3xdx

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  12. If vec a =3 hat i -hat j +hat k, vec b= hat i +3hat j - hat k and ve...

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  13. Integrate the following int dx/(x^2+10x+9)

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  14. If vec a,vec b,vec c are any three vectors, prove that vec a xx (vec b...

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  15. For any vector vec a, prove that hat i xx (vec a xx hat i)+ hat j xx (...

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  16. If a,b and c are three non-zero vectors such that a*(bxxc)=0 and b and...

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  17. Integrate the following int xcos5xdx

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  18. What is the magnitude of a unit vector ?

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  19. 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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  20. Does |quad vec a|= |quad vec b| imply vec a= vec b?

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