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Prove that vectors vecu=(al+a(1)l(1))h...

Prove that vectors
`vecu=(al+a_(1)l_(1))hati+(am+a_(1)m_(1))hatj + (an+a_(1)n_(1))hatk`
`vecv=(bl+b_(1)l_(1))hati+(bm + b_(1)m_(1))hatj+(bn+b_(1)n_(1))hatk`
`vecw=(cl+c_(1)l_(1))hati+(cm+c_(1)m_(1))hatj+(cn+c_(1)n_(1))hatk`

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`[vecuvecv vecw]=|{:(al=a_(1)l_(1),am+a_(1)m_(1),an+a_(1)n_(1)),(bl+b_(1)l_(1),bn+b_(1)m_(1),bn+b_(1)n_(1)),(cl+c_(1)l_(1),cm+c_(1)m_(1),cn+c_(1)n_(1)):}|`
`=|{:(a,a_(1),0),(b,b_(1),0),(c,c_(1),0):}||{:(l,l_(1),0),(m,m_(1),0),(n,n_(1),0):}|=0`
Therefore, the given vectors are coplanar.
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. Prove that vectors vecu=(al+a(1)l(1))hati+(am+a(1)m(1))hatj + (an+a(...

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  2. Find |veca|and|vecb|, if (veca+vecb)*(veca-vecb)=8and|veca|=8|vecb|.

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  3. Show that |veca|vecb+|vecb|veca is perpendicular to |veca|vecb-|vecb|...

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

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  5. If |a|=3,|b|=4a n d the angle between aa n db is 120^0 , then find the...

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  6. If vectors hati-2xhatj-3yhatk and hati+ 3 x hatj + 2yhatk are orthogon...

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  7. Let veca vecb and vecc be pairwise mutually perpendicular vectors, suc...

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  8. If veca+vecb+vecc =0, |veca|=3, |vecb|=5, |vecc|=7 then the angle betw...

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  9. If the angle between unit vectors veca and vecb is 60^(@) . Then find ...

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  10. Let vecu=hai+hatj,vecv=hati-hatj and vecw=hati+2hatj+3hatk. If hatn is...

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  11. A , B , C , D are any four points, prove that vec A B dot vec C D+ ...

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  12. P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(,-2,-1), then find the projection...

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  13. If the vectors 3 vec p+ vec q ;5p-3 vec qa n d2 vec p+ vec q ;3 vec p-...

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  14. Let vecA and vecB be two non-parallel unit vectors in a plane. If (alp...

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  15. If veca ,vecb, vec c are three vectors such that veca + 2 vecb + vecc ...

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  16. If veca and vecb are unit vectors, then find the greatest value of |ve...

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  17. Constant forces P1= hat i+ hat j+ hat k ,P2= hat i+2 hat j- hat ka n d...

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  18. Find |veca|and|vecb|, if (veca+vecb)*(veca-vecb)=8and|veca|=8|vecb|.

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  19. If A ,B ,C ,D are four distinct point in space such that A B is not...

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  20. If veca=2hati+ 3hatj-5hatk,vecb =m hati+nhatj +12 hatk and veca xx vec...

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  21. If |veca|=2, |vecb|=5 and |vecaxxvecb|=8 then find the value of veca.v...

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