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Fo any four vectors overlinea,overlineb,...

Fo any four vectors `overlinea,overlineb,overlinec` and `overlined`, prove that
(i) `(overlineatimesoverlineb)times(overlinectimesoverlined)=[overline(ac)overlined]overlineb-[overlineboverlinecoverlined]overlinea` and (ii) `(overlineatimesoverlineb)times(overlinectimesoverlined)=[overlineaoverline(bd)]overlinec-[overlineaoverlineboverlinec]overlined`

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IF overlinea=2overlinei+overlinej-overlinek,overlineb=-overlinei+2overlinej-4overlinek,overlinec=overlinei+overlinej+overlinek then find (overlinea times overlineb).(overlineb times overlinec)

IF overlinea=2overlinei-overlinek,overlineb=-overlinei+2overlinej-4overlinek,overlinec=overlinei+overlinej+overlinek then find (overlineatimesoverlineb).(overlinebtimesoverlinec)

IF overlinea,overlineb,overlinec are non-coplanar, then prove that the points with position vectors 2overlinea+3overlineb-overlinec,overlinea-2overlineb+3overlinec,3overlinea+4overlineb-2overlinec,overlinea-6overlineb+6overlinec are coplanar.

Show that the four points -overlinea+4overlineb-3overlinec,3overlinea+2overlineb-5overlinec,-3overlinea+8overlineb-5overlinec,-3overlinea+2overlineb+overlinec are coplanar, where overlinea,overlineb,overlinec are non-coplanar vectors.

IF overlinea+overlineb+overlinec=overline0,|overlinea|=3|overlineb|=5 and |overlinec|=7 , then find the between overline a and overlineb .

overlinea=2overlinei-overlinej+overlinek,overlineb=overlinei-3overlinej-5overlinek . Find the vector overlinec such that overline a ,overline b & overline c form the sides of a triangle.

SRISIRI PUBLICATION-IPE:MARCH-2018(AP)-QUESTIONS
  1. IF the vectors -3overlinei+4overlinej+lamdaoverlinek,muoverlinei+8over...

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  2. Find the vector equation of plane passing through Points (0,0,0) , (0,...

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  3. Find the angle between the vectors overlinei+2overlinej+3overlinek and...

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  4. Find sin330^@.cos120^@+ cos210^@.sin300^@

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  5. Find the extreme values of cos 2x+cos^2x

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  6. Prove that cosh2x=2cosh^(2)x-1

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  7. IF A=[{:(7,-2),(-1,2),(5,3):}].B=[{:(-2,-1),(4,2),(-1,0):}] then find ...

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  8. Show that the four points -overlinea+4overlineb-3overlinec,3overlinea+...

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  9. Let overlinea and overlineb be vectors, satisfying |overlinea|=|overli...

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  10. If A is not an integral multiple of (pi)/(2), prove that (i) tan A +...

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  11. Solve sqrt3sintheta-costheta=sqrt2

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  12. Prove that Sin^-1""4/5+Sin^-1""5/13+Sin^-1(16/65)=pi/2

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  13. If a = (b-c) "sec" theta, then prove that tan theta = (2sqrt(bc))/(b-c...

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  14. If f: A to B, g:B to C are two bijective functions then prove that gof...

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  15. Using the P.M.I 2prove that 1/1.3+1/3.5+1/5.7+....+n terms=n/(2n+1)

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  16. Show that |{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^3

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  17. Solve the system of equations 2x-y+3z=9,x+y+z=6,x-y+z=2 using Gauss J...

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  18. Fo any four vectors overlinea,overlineb,overlinec and overlined, prove...

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  19. If A,B,C are angles in a triangle , then prove that cosA+cosB+cosC=1+4...

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  20. Show that r+r(3)+r(1)-r(2)=4RcosB.

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