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Show that the points A(2 hat i - hat j +...

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.

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Show that the points A(-2 hat i+ 3 hat j + 5 hat k) , B(hat i+ 2 hat j+ 3 hat k) and C(7 hat i-hat k) are collinear.

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Calculate the product ((hat i- 2 hat j+ 3 hat k) cross (2 hat i+ hat j- 3 hat k)) * (-3 hat i+ hat j+ 2 hat k ) .

Show that the points A, B and C with position vectors, vec a= 3hat i-4 hatj -4 hat k, vec b= 2 hat i -hatj +hat k and vec c =hat i-3hat j-5 hat k , respectively, form the vertices 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.

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.

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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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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Show that the points A(2 hat i - hat j + hat k), B(hat i - 3 hat j- 5 ...

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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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