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If vec a, vec b and vec c are non-coplan...

If `vec a`, `vec b` and `vec c` are non-coplanar (independent) vectors, prove that the vectors `vec a- 2 vec b+ 3 vec c`, `-2 vec a + 3 vec b- 4 vec c` and `vec a -vec b+ 2 vec c ` are also linearly independent.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Show that the points (1,1,1),(2,-1,2),(-1,2,2) and (2,2,-1) are coplan...

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  2. Show that the points A(4,5,1), B(0,-1,-1), C(3,9,4) and D(-4,4,4) are ...

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  3. If vec a, vec b and vec c are non-coplanar (independent) vectors, prov...

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  4. Find vec v underset 1 * vec v underset 2 when vec v underset 1= 4 hat ...

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  5. Find vec v underset 1 * vec v underset 2 when vec v underset 1= (1,3,5...

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  6. Find the angle between the vectors: vec v underset 1= hat i-2 hat j-...

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  7. Find the angle between the vectors: vec v underset 1= (3,5,4) and ve...

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  8. Find the value of lambda so that the vectors vec a= 3 hat i + 3 hat j-...

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

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  10. Find the value of a for which the vector 3 hat i+ 2 hat j+ 9 hat k and...

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  11. Find the value of a for which the vector 3 hat i+ 2 hat j+ 9 hat k and...

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

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  13. Find the angles which the vector 3 hat i- 6 hat j+ 2 hat k makes the c...

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  14. If vec a and vec b are two vectors such that |quad vec a + vec b|= |qu...

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  15. If vec a and vec b are two vectors such that |quad vec a + vec b|= |qu...

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  16. If vec a is any vector in space, then show that vec a= ( vec a* hat i...

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  17. If the vertices A,B,C of triangle ABC have position vectors (1,2,3), (...

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  18. If hat i+ hat j+ hat k,2 hat i+ 5 hat j, 3 hat i+ 2 hat j- 3 hat k and...

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

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  20. Find the projection (vector) of the vector 7 hat i+ hat j- 4 hat k on ...

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