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Prove that the three vectors 3 hat i +ha...

Prove that the three vectors `3 hat i +hat j+ 2 hat k`, `hat i-hat j-hat k` and `hat i +5 hat j- 4 hat k` are at right angle to one another.

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Prove that the vectors vec a= hat i- 3 hat j - 5 hat k , vec b= 2 hat i- hat j+ hat k and vec c= hat i+ 2 hat j+ 6 hat k from of a right angled triangle.

Show that the vectors vec a=2 hat i- hat j+ hat k , vec b=hat i-3 hat j-5 hat k , vec c=3 hat i-4hat j-4 hat k form a right angled triangle.

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

Show that the points A(2 hat i - hat j + hat k) , B(hat i - 3 hat j- 5 hat k ) and C(3 hat i - 4 hat j- 4 hat k) are the vertices of a right angled triangle.

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

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Prove that the points whose position vectors are hat i - hat j+ hat k , 2 hat i+ 3 hat j+ hat k , hat i+ 2 hat j+ 3 hat k , -2 hat j+ 3 hat k lie in the same plane.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Prove that the three vectors 3 hat i +hat j+ 2 hat k, hat i-hat j-hat ...

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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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