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Find the volume of the parallelepiped wh...

Find the volume of the parallelepiped 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 , vec c=3 hat i- hat j+2 hat k` ` vec a=2 hat i+3 hat j+4 hat k , vec b= hat i+2 hat j- hat k , vec c=3 hat i- hat j-2 hat k` ` vec a=11 hat i , vec b=2 hat j- hat k , vec c=13 hat k` ` vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat k , vec c= hat i+2 hat j- hat k`

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Find the volume of the parallelepiped whose coterminous edges are represented by the vector: vec a=2hat i+3hat j+4hat k,vec b=hat i+hat i+2hat j-hat k,vec c=3hat i-hat j+2hat k

Find the volume of the parallelepiped whose coterminous edges are represented by the vector: vec a=2hat i-3hat j+4hat k,vec b=hat i+hat i+2hat j-hat k,vec c=3hat i-hat j-2hat k

Find the volume of the parallelepiped whose coterminous edges are represented by the vector: vec a=hat i+hat j+hat k,vec b=hat i-hat j+hat k,vec c=hat i+2hat j-hat k

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

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

Show that each of the following triads of vectors are coplanar: vec a= hat i+2 hat j- hat k , vec b=3 hat i+2 hat j+7 hat k , vec c=5 hat i-6 hat j+5 hat k vec a=-4 hat i-6 hat j-2 hat k , vec b=- hat i+4 hat j+3 hat k , vec c=8 hat i- hat j+3 hat k hat a= hat i-2 hat j+3 hat k , vec b=-2 hat i+3 hat j-4 hat k , vec c= hat i-3 hat j+5 hat k

[vec a,vec b,vec c], when vec a=2hat i-3hat j+4hat k,vec b=hat i+2hat j-hat k and vec c=3hat i-hat j+2hat k

If vec a=3hat i-hat j-4hat k,vec b=2hat i+4hat j-3hat k and vec c=hat i+2hat j-widehat k, find |3vec a-2hat b+4hat c|

Find vec a.( vec bxx vec c)\ if\ vec a=2 hat i+ hat j+3 hat k ,\ vec b=- hat i+2 hat j+ hat k\ a n d\ vec c=3 hat i+ hat j+2 hat kdot

Find the area of the rriangle formed by the tips of the vectors, vec a= (2 hat I - hat j+ 3 hat k), vec b= 4 hat I + 3 hat j-hat k , vec C= 3 hat I - hat j + 2 hat k .

A DAS GUPTA-Product of three or more Vectors-Exercise
  1. Prove that hat ixx( vec axx hat i) hat jxx( vec axx hat j)+ hat kxx( ...

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  2. If vecaxx(vecbxxvecc)+(veca*vecb)vecb=(4-2beta-sinalpha)vecb+(beta^2-...

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  3. Let vec abe a unit vector and vec ba non-zero vector not parallel to v...

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  4. For any vector vec a , prove that | vec axx hat i|^2+| vec axx hat j|...

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  5. If vectors b ,ca n dd are not coplanar, then prove that vector ( ve...

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  6. If vec a, vecb and vec c are three conterminuous edges of a parallelo...

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  7. Let vec a , vec b ,a n d vec c be non-coplanar unit vectors, equal...

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  8. If vec a=vec i + vec j + vec k, vec b=vec i - vec j + vec k and vec c=...

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  9. If the volume of a parallelopiped, whose three coterminous edges are -...

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  10. Find the volume of the parallelepiped whose coterminous edges are r...

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  11. The points (3,6,9), (1,2,3), (2,3,4) and (4,6,lambda) are coplanar if ...

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  12. If vec xdot vec a=0, vec xdot vec b=0a n d vec xdot vec c=0 for some ...

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  13. Let veca,vecb and vecc be three vectors having magnitudes 1, 1 and 2 r...

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  14. The scalar vec Adot( vec B+ vec C)xx( vec A+ vec B+ vec C) equals 0 b...

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  15. Let a,b,c be distinct non zero numbers. If the vectors a vec i + a ve...

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  16. The vectors vecaxx(vecbxxvecc), vecbxx(veccxxveca) and veccxx(vecaxxve...

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  17. vec p , vec q ,a n d vec r are three mutually perpendicular vectors of...

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  18. In each of the following, one or more options ar correct. Choose the ...

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  19. If vec a= vec p+ vec q , vec pxx vec b=0a n d vec qdot vec b=0, then ...

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  20. Given | vec a|=| vec b|=1a n d| vec a+ vec b|=3. If vec c is a vector...

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