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Vectors vec a,vec b, vec c and vec d are...

Vectors `vec a`,`vec b`, `vec c` and `vec d` are given by `vec a= hat i+ hat j+ hat k`, `vec b= 2 hat i+ 3 hat j`, `vec c= 3 hat i+ 5 hat j- 2 hat k` and `vec d= - hat j+ hat k`. Show that the vectors `vec b- vec a ` and `vec d- vec c` are parallel and find the ratio of their lengths.

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If vec a= hat i+ 2hat j- 3 hat k and vec b= 3 hat i- hat j+ 2 hat k , show that the vectors vec a+ vec b and vec a- vec b are at right angles.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Vectors vec a,vec b, vec c and vec d are given by vec a= hat i+ hat j+...

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  2. Classify the following physical quantities into scalars and vectors: ...

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  3. Classify the following physical quantities into scalars and vectors: ...

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  4. Classify the following physical quantities into scalars and vectors: ...

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  5. Classify the following physical quantities into scalars and vectors: ...

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  6. Classify the following physical quantities into scalars and vectors: ...

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  7. Classify the following physical quantities into scalars and vectors: ...

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  8. Classify the following physical quantities into scalars and vectors: ...

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  9. Classify the following physical quantities into scalars and vectors: ...

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  10. Classify the following physical quantities into scalars and vectors: ...

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  11. Find lambda in R such that |quad lambda vec a|=1, vec a being a non-ze...

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  12. If |quad vec a|=2, find |quad 4 vec a |, |10 vec a| and |(-5 ) vec a |...

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  13. Is it possible that |quad vec a+ vec b|= |quad vec a|+ |quad vec b|? I...

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  14. If vec a = vec b, is it true that |quad vec a|=|quad vec b| ?

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

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  16. If A,B,C,D are the points with position vectors vec a,vec b, 3 vec a+ ...

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  17. If vec c= 3 vec a + 4 vec b and 2 vec c = vec a- 3 vec b, show that ve...

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  18. If the position vector of a point A is vec a + 2 vec b and vec a divi...

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  19. If ABC is triangle and D is the mid-point of [BC], prove that vec AB +...

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

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  21. If vec a = 5hat i - hat j- 2hat k and vec b =5 hat i+ hat j - 2 hat k,...

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