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Find the projection of the vector vec a ...

Find the projection of the vector `vec a = 2 hat i+ 3 hat j+ 2 hat k` on the vector `vec b= hat i+ 2 hat j+ hat k`.

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Find a unit vector in the direction of the sum of the vectors: vec a= 2 hat i+ 2 hat j+ 5 hat k and vec b= 2 hat i+ hat j- 3 hat k .

Find a vector of magnitude 5 units, and parallel to the resultant of the vectors vec a =2 hat i+3 hat j- hat k and vec b= hat i-2 hat j+hat k .

Find a unit vector in the direction of the sum of the vectors: vec a= - hat i+ hat j+ hat k and vec b= 2 hat i+ hat j- 3 hat k .

Find the area of the parallelogram whose adjacent sides are determined by the vectors vec a = hat i - hat j+ 3 hat k and vec b = 2hat i - 7hat j+ hat k

Find the value of lambda so that the vectors vec a= 3 hat i + 3 hat j- lambda hat k and vec b= 2 hat i- hat j+ hat k are perpendicular to each other.

Find a unit vector parallel to the sum of the vector vec a= hat i+ hat j+ hat k , vec b= 3 hat i+ hat j- 4 hat k and vec c=-2 hat i- hat j-hat k .

Find the volume of the Parallelopiped whose coterminous edges are represented by the vectors vec a = 2 hat i- 3 hat j + 4 hat k, vec b= hat i +2 hat j- hat k and vec c = 3 hat i -hat j +2 hat k .

Find vec a* vec b if vec a=3 hat i+4 hat j-2 hat k and vec b=-2 hat i+ 2 hat j + hat k

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

Find the sine of the angle between the vectors vec a =3 hat i+hat j+2 hat k and vec b =2hat i-2 hat j+4 hat k .

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find the projection of vec AB on vec PQ where P,Q,A,B are the points (...

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  2. If A,B,C,D are the points with position vectors hat i+ hat j-hat k, 2 ...

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  3. Find the projection of the vector vec a = 2 hat i+ 3 hat j+ 2 hat k on...

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  4. Find the projection of thevector hat i+ 3 hat j+ 7 hat k on the vector...

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  5. Prove that the vectors vec a= hat i- 3 hat j - 5 hat k , vec b= 2 hat ...

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  6. If A,B,C have position vectors (0,1,1),(3,1,5),(0,3,3) respectively, p...

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  7. Prove Cauchy- Schwarz inequality |quad vec a* vec b|<|quad vec a||quad...

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  8. For any two vectors vec a and vec b, prove that (vec a* vec b)^ 2 le |...

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  9. If |quad vec a|=1, |quad vec b|=1 and |quad vec a+ vec b|=1, prove tha...

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  10. If |quad vec a+ vec b|=|quad vec a- vec b|, prove that vec a and vec b...

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  11. If (vec a+ vec b)* (vec a- vec b)=0, show that |quad vec a|=|quad vec ...

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  12. If vec a and vec b are any two vectors, then prove that |quad vec a+ v...

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  13. Prove that two proper vectors vec a and vec b are the right angles iff...

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  14. If vec a,vec b,vec c are three non-coplanar vectors and vec d* vec a ...

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  15. Find a vector vec c such that vec c*(hat i+ hat j)= 2, vec c* (hat i- ...

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  16. Find a vector vec c such that vec c. hat i = vec c. hat j= vec c . hat...

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  17. If vec c is normal to vec a and vec b, show that vec cis normal to ve...

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  18. If vec a, vec b, vec c are three vectors such that |quad vec a|=5,|,qu...

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  19. If vec a,vec b,vec c are mutually perpendicular unit vectors , then f...

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  20. Prove that, in any triangle ABC, cos B=(c^2+a^2-b^2)/(2ca).

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