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Let vec a = a1 hat i + a2 hat j+ a3 hat...

Let `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 ; vec c= c_1hat i + c_2 hat j+ c_3 hat k` be three non-zero vectors such that `vec c` is a unit vector perpendicular to both `vec a & vec b`. If the angle between `vec a and vec b` is `pi/6` , then `|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|^2=`

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Let 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 ka n d vec c=c_1 hat i+c_2 hat j+c_3 hat k be three non-zero vectors such that vec c is a unit vector perpendicular to both vec aa n d vec b . If the angle between aa n db is pi/6, then prove that |a_1a_2a_3b_1b_2b_3c_1c_2c_3|=1/4(a1 2+a2 2+a3 2)(b1 2+b2 2+b3 2)

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\ a n d\ 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

If vec A = hat i + 3 hat j + 2 hat K and vec B = 3 hat i + hat j + 2 hat k , then find the vector product vec A xx vec B .

let vec a=hat i+hat j-hat k and vec b=hat i-hat j-hat k and vec c be a unit vector perpendicular to vec a and coplanarwith vec a and vec b then vec c is

vec a = a_1 hat i a_2 hat j a_3 hat k |a| = 1 , &, vec a. vec b = 2 vec b = b_1 hat i b_2 hat j b_3 hat k |b| = 4 vec c = 2 (vec a times vec b) - 3 vec b then angel between vec c and vec b

The unit vector perpendicular to vec A = 2 hat i + 3 hat j + hat k and vec B = hat i - hat j + hat k is

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

If vec a= hat i+ hat j+ hat k , vec b=2 hat i- hat j+3 hat k a n d vec c= hat i-2 hat j+ hat k find a unit vector parallel to 2 vec a- vec b+3 vec cdot

If vec A=hat I + 2 hat j -3 hat k , vec B =2 hat I -hat j + hat k and vec Chat I -3 hat j + 2 hat k , then find vec A xx ( vec B xx vec C).

A DAS GUPTA-Product of three or more Vectors-Exercise
  1. If the three vectors vec a+ vec b , vec b+ vec c and vec c+ vec a ar...

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  2. Prove that ( vec a- vec b)dot{( vec b- vec c)xx( vec c- vec a)}=0

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  3. Let vec a = a1 hat i + a2 hat j+ a3 hat k;vec b = b1 hat i+ b2 hat j+...

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  4. lf vec a,vec b,vec c , vec a', vec b',vec c', are two sets of non-...

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  5. Let vec(a),vec(b)andvec(c) be three non-coplanar vectors and let vec(p...

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  6. If vec a,vec b,vec c are three vectors such that vec a+vec b+vec c=vec...

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  7. Prove that hat ixx( vec axx hat i) hat jxx( vec axx hat j)+ hat kxx( ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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