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Let V be the volume of the parallelepipe...

Let V be the volume of the parallelepiped formed by the vectors `vec a = a_i hat i +a_2 hat j +a_3 hat k` and `vec b =b_1 hat i +b_2 hat j +b_3 hat k` and `vec c = c_1 hat i + c_2 hat j + c_3 hat k` . If `a_r, b_r and c_`r, where r = 1, 2, 3, are non-negative real numbers and `sum_(r=1)^3(a_r+b_r+c_r)=3L` show that `V le L^3`

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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+2 hat j- hat k .

Find the volume of the parallelepiped whose coterminous edges are represented by the vector: 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 .

Find the volume of the parallelepiped whose coterminous edges are represented by the vector: 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 .

If vec a=a_1 hat i+a_2 hat j+a_3 hat k ,\ vec b=b_1 hat i+b_2 hat j+b_3 hat k and vec c=c_1 hat i+c_2 hat j+c_3 hat k , then verify that vec axx( vec b+ vec c)= vec axx vec b+ vec axx vec c

Show that the vectors vec a=-2 hat i-2 hat j+4 hat k ,\ vec b=-2 hat i+4 hat j-2 hat k\ a n d\ vec c=4 hat i-2 hat j-2 hat k are coplanar.

Find the projection of vec b+ vec c on vec a , where vec a = 2 hat i-2 hat j+ hat k , vec b = hat i+2 hat j-2 hat k and vec c=2 hat i- hat j+4 hat k .

Find the volume of the parallelopiped whose edges are represented by 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)

Find lambda so that the vectors vec a=2 hat i- hat j+ hat k ,\ vec b= hat i+2 hat j-3 hat k\ a n d\ vec c=3 hat i+lambda hat j+5 hat k are coplanar.

If the vectors vec (a) = 2 hat (i) - hat (j) + hat (k) , vec ( b) = hat (i) + 2 hat (j) - 3 hat (k) and vec(c ) = 3 hat (i) + lambda hat (j) + 5 hat (k) are coplanar , find the value of lambda

Find | vec a xx vec b|, if vec a=2 hat i+ hat j+3 hat k and vec b=3 hat i+5 hat j-2 hat k .

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. If aa n db are nonzero non-collinear vectors, then [ vec a vec b hat...

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  2. ( vec a+ vec b)dot( vec b+ vec c)xx( vec a+ vec b+ vec c)= [ vec a\ ...

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  3. A vector of magnitude 10 along the normal to the curve 3x^2+8x y+2y^2-...

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  4. If a( vecalphaxx vecbeta)+b( vecbetaxx vecgamma)+c( vecgammaxx vecalph...

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  5. If ( vec axx vec b)xx( vec bxx vec c)= vec b ,w h e r e vec a , vec b ...

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  6. If vec a , vec b , vec c are any three noncoplanar vector, then ( ...

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  7. If vec x+ vec cxx vec y= vec aa n d vec y+ vec cxx vec x= vec b ,w h ...

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  8. If vec aa n d vec b are two unit vectors incline at angle pi//3 , ...

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  9. If vec a and vec b are orthogonal unit vectors, then for a vector ...

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  10. Let V be the volume of the parallelepiped formed by the vectors vec a ...

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  11. Find 3-dimensional vectors vec v1,vec v2,vec v3 satisfying vec v1* ve...

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  12. Let vec ua n d vec v be unit vectors such that vec uxx vec v+ vec u=...

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  13. For any two vectors vec ua n d vec v prove that ( vec u. vec v)^2+| ...

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  14. If the incident ray on a surface is along the unit vector vec v, the r...

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  15. P1n dP2 are planes passing through origin L1a n dL2 are two lines o...

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  16. If vec a , vec b , vec ca n d vec d are distinct vectors such that ...

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  17. Given two vectors vec a=- hat i+2 hat j+2 hat ka n d vec b=-2 hat i+ ...

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  18. Let vec V=2 hat i+ hat j- hat ka n d vec W= hat i+3 hat kdot If vec ...

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  19. If the vectors vec a, vec b, vec c are non-coplanar and l,m,n are dist...

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  20. If vec a , vec ba n d vec c are unit coplanar vectors, then the sc...

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