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Show that the vectors 2 hat i -3 hat j +...

Show that the vectors `2 hat i -3 hat j +4 hat k and -4 hat i +6 hat j -8 hat k` are collinear.

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Find the angle between the vectors 2 hat i -hat j+ hat k and 3 hat i +4hat j - hat k

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

Find the angle between the vectors 3 hat i-2 hat j -6 hat k and 4 hat i-hat j-8 hat k .

Find a vector of magnitude 6 units which is at right angles to both the vectors 2 hat i- hat j +2 hat k and 4 hat i- hat j+3 hat k

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.

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

Show that the vectors vec a = hat i- 3 hat j+ 2 hat k , vec b= 2 hat i- 4 hat j- 4hat k and vec c= 3 hat i+ 2 hat j- 3hat k are linearly independent.

Find a unit vector perpendicular to both the vectors 4 hat i-hat j+3 hat k and -2 hat i+hat j-2 hat k .

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Show that the vectors 2 hat i -3 hat j +4 hat k and -4 hat i +6 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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