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Prove that the points whose position vec...

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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Prove that the points whose position vectors are 6 hat i - 7 hat j, 16 hat i -29 hat j -4 hat k , 3 hat j -6 hat k and 2 hat i+5 hat j +10 hat k are coplanar.

Show that the point A,B,C and D whose position vectors are respectively 2 hat i+ 4 hat j+ 2 hat k , hat i+ 2 hat j+ hat k , 3 hat i+ hat j- 3 hat k and 4 hat i+3 hat j - 2 hat k are the vertices of a paralleogram (use vector method).

Show that the points A,B and C whose position vectors are repectively 2 hat i+ hat j- hat k , 3 hat i- 2 hat j+ hat k and hat i+ 4 hat j- 3 hat k are collinear.

Prove that the vectors 2 hat i- hat j+ hat k , hat i- 3 hat j- 5 hat k and 3 hat i- 4 hat j- 4 hat k are coplanar.

Show that the four points having position vectors 6 hat i-7 hat j, 16 hat i-19 hat j -4hat k, 3 hat j-6 hat k, 2 hat i+5 hat j +10 hat k are not coplanar.

Find λ if the vectors hat i-hat j+ hat k, 3 hat i+ hat j+ 2 hat k and hat i+ λ hat j- 3 hat k are coplanar.

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

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

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.

Find the projection (vector) of the vector 7 hat i+ hat j- 4 hat k on 2 hat i+ 6 hat j+ 3 hat k .

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. The sides of a parallelogram represent the vectors 2 hat i- 4 hat j+ 5...

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  2. Let vec a= 2 hat i- 2 hat j+ hat k, vec b= 2 hat i+ 3 hat j+ 6 hat k a...

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  3. Prove that the points whose position vectors are hat i - hat j+ hat k,...

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  4. Prove that the vectors vec a = hat i- 2 hat j+ hat k, vec b= -2 hat i+...

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  5. Show that the points (1,1,1),(2,-1,2),(-1,2,2) and (2,2,-1) are coplan...

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

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

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

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

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

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

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

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

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

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

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

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

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

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