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If vectors hati-2xhatj-3yhatk and hati+ ...

If vectors `hati-2xhatj-3yhatk and hati+ 3 x hatj + 2yhatk` are orthogonal to each other, then find the locus of th point (x,y).

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It is given that vectors `hati - 2xhatj - 3yhatk and hati + 3x hatj + 2yhatk` are orthogonal , therefore,
`(hati-2xhatj - 3yhatk).(hati+3xhatj+2yhatk)=0`
` or 1-6x^(2)-6y^(2)=0`
`or bx^(2)+6y^(2)=1` whiche is a circle.
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If the vertices A,B, C of a triangle ABC are (1,2,3),(-1, 0,0), (0, 1,...

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

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

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

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

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

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

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

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  9. 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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  10. 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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  11. Let vecA and vecB be two non-parallel unit vectors in a plane. If (alp...

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

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

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

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

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

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

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

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  19. If veca xx vecb = vecb xx vecc ne 0 where veca , vecb and vecc are co...

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  20. If veca = 2vecj+3vecj-veck, vecb =-veci+2vecj-4veck and vecc=veci + ve...

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