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If the vectors 2 hat i-3 hat j , hat i+ ...

If the vectors `2 hat i-3 hat j , hat i+ hat j- hat ka n d3 hat i- hat k` form three concurrent edges of a parallelepiped, then find the volume of the parallelepiped.

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If the vectors 3 hat i+m hat j+ hat k\ a n d\ 2 hat i- hat j-8 hat k are orthogonal, find mdot

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Find the altitude of a parallelepiped whose three coterminous edtges are vectors vec A= hat i+ hat j+ hat k , vec B=2 hat i+4 hat j- hat ka n d vec C= hat i+ hat j+3 hat kw i t h vec Aa n d vec B as the sides of the base of the parallepiped.

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If the two diagonals of one its faces are 6 hat i+6 hat ka n d4 hat j+2 hat k and of the edges not containing the given diagonals is c=4 hat j-8 hat k , then the volume of a parallelepiped is a. 60 b. 80 c. 100 d. 120

Dot product of a vector with hat i+ hat j-3 hat k ,\ hat i+3 hat j-2 hat k\ a n d\ 2 hat i+ hat j+4 hat k are 0, 5 and 8 respectively. Find the vector.

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Show that the vectors veca= hat i-2 hat j+3 hat k , vecb=-2 hat i+3 hat j-4 hat ka n d vec c= hat i-3 hat j+5 hat k are coplanar.

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. Let A,B,C be three unit vectors and A.B= A.C=0. If the angel between ...

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  2. The position vectors of the four angular points of a tetrahedron ar...

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  3. If the vectors 2 hat i-3 hat j , hat i+ hat j- hat ka n d3 hat i- hat ...

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  4. If vec u , vec v and vec w are three non-coplanar vectors, then pro...

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  5. Find the value of a so that the volume of the parallelepiped formed...

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  6. If vec a=2 hat i+3 hat j-5 hat k , vec b=m hat i+n hat j+12 hat k and...

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  7. Prove that [ vec l vec m vec n][ vec a vec b vec c]=| (vec l. vec a, v...

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  8. Find the altitude of a parallelepiped whose three coterminous edtge...

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  9. If vec a and vec b are two vectors such that | vec a|=2, |vecb|=3 and...

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  10. Prove that vec R+([ vec Rdot( vecbetaxx( vecbetaxx vecalpha))] vecalp...

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  11. If vec a , vec b ,and vec c are non-coplanar unit vectors such that...

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  12. If vec r. vec a=0, vec r. vec b=1 \ and \ [[ vec r ,vec a, vec b]]=1,...

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  13. If vec a and vec b are two given vectors and k is any scalar, then fi...

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  14. vec a , vec ba n d vec c are three non-coplanar ,non-zero vectors an...

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  15. If vector vec x satisfying vec xxx vec a+( vec xdot vec b) vec c= ve...

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  16. Let hat a , hat b ,and hat c be the non-coplanar unit vectors. The...

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  17. Find the vector of length 3 unit which is perpendicular to hat i+ h...

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  18. If vec b is not perpendicular to vec c , then find the vector vec r...

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  19. If vec a , vec ba n d vec c are three non coplanar vectors, then ( ...

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  20. Let vec a , vec b and vec c be three non-zero vectors such that ve...

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