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For any four vectors, prove that ( ve...

For any four vectors, prove that `( veca × vecb )×( vecc × vecd )=[ veca vecc vecd ] vecb −[ vecb vecc vecd ] veca `

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If a ,ba n dc are three non-cop0lanar vector, non-zero vectors then the value of ( veca . veca ) vecb × vecc +( veca . vecb ) vecc × veca +( veca . vecc ) veca × vecb .

If veca, vecb and vecc are three non-coplanar non-zero vectors, then prove that (veca.veca) vecb xx vecc + (veca.vecb) vecc xx veca + (veca.vecc)veca xx vecb = [vecb vecc veca] veca

If veca + 2 vecb + 3 vecc = vec0 " then " veca xx vecb + vecb xx vecc + vecc xx veca=

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for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc) xx (vecc -veca) =

Prove that: (vecaxxvecb)xx(veccxxvecd)+(vecaxxvecc)xx(vecd xx vecb)+(vecaxxvecd)xx(vecbxxvecc) = -2[vecb vecc vecd] veca

If veca .vecb =beta and veca xx vecb = vecc ," then " vecb is

Prove that [veca+vecb vecb+vecc vecc+veca]=2[veca vecb vecc]

If vec a , vec b and vec c are such that veca xx vecb = vecc and vecb xx vec c = vec a , prove that veca , vecb and vecc are mutually perpendicular |vecb| =1 and |vecc| = |veca| .

If veca, vecb, vecc and vecd are distinct vectors such that veca xx vecc = vecb xx vecd and veca xx vecb = vecc xx vecd . Prove that (veca-vecd).(vecb-vecc)ne 0

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
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  2. Prove that vectors vec u=(a l+a1l1) hat i+(a m+a1m1) hat j+(a n+a1n1)...

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  3. For any four vectors, prove that ( veca × vecb )×( vecc × vec...

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  4. If vec ba n d vec c are two-noncollinear vectors such that vec a...

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  5. If the vertices A,B,C of a triangle ABC are (1,2,3),(-1,0,0) ,(0,1,2) ...

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  6. Let vec a , vec ba n d vec c be pairwise mutually perpendicular vec...

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  7. Show that | vec a| vec b+| vec b| vec a is a perpendicular to | vec a|...

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  8. If |veca|=3, |vecb|=4 and the angle between veca and vecb is 120^(@) ....

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  9. If vec a , vec b ,a n d vec c be three non-coplanar vector and p,q,...

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  10. Find | -> a| and | -> b| , if ( -> a+ -> b)dot( -> a- -> b)=8 an...

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  11. Let vec a , vec b ,a n d vec ca n d vec a^' , vec b^' , vec c ' are r...

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  12. If vec a , vec b and vec c are three non-coplanar vectors, then ( v...

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  13. Find the vector equation of the plane passing through the points havin...

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  14. If vec axx vec b= vec bxx vec c!=0,w h e r e vec a , vec b ,a n d vec...

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  15. If vec a=2 vec i+3 vec j- vec k , vec b=- vec i+2 vec j-4 vec k a n d...

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  16. If the vectors vec c , vec a=x hat i+y hat j+z hat k and vec b= hat j...

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  17. Given that vec adot vec b= vec adot vec c , vec axx vec b= vec axx ve...

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  18. If | vec a|=5,| vec a- vec b|=8 and | vec a+ vec b|=10 , then find | v...

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  19. If A ,B ,C ,D are four distinct point in space such that vec(A B) is...

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  20. 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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