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Using vectors, prove that cos(alpha-be...

Using vectors, prove that
`cos(alpha-beta)=cosalpha cosbeta+sinalphasinbeta`

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Using vectors, prove that sin (alpha+beta)=sin alpha cos beta+ cos alpha sin beta .

Prove by vectors that : cos (alpha - beta) = cos alpha cos beta+ sin alpha sin beta .

Using vectors prove that sin(alpha - beta) = sin alpha cos beta- cos alpha sin beta .

Prove by vectors that : cos (alpha + beta) = cos alpha cos beta- sin alpha sin beta .

Prove that: (cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=4cos^2((alpha-beta)/2)

If cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-3/2 , prove that cosalpha+cosbeta+cosgamma= sinalpha+ sinbeta+singamma=0

If tan beta= (Q sin alpha)/(P+Q cos alpha) , prove that : tan (alpha-beta)= (P sin alpha)/(Q+P cos alpha) .

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Using properties of determinants, prove that: |[sinalpha,cosalpha,cos(alpha+delta)],[sinbeta,cosbeta,cos(beta+delta)],[singamma,cosgamma,cos(gamma+delta)]| = 0

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BETTER CHOICE PUBLICATION-VECTOR ALGEBRA -PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE (MCQ)
  1. Find the projection of hati-hatj on the line represented by the vector...

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  2. For given vectors,veca=2hati-hatj+2hatk and vecb=-hati+hatj-hatk , fin...

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  3. Using vectors, prove that cos(alpha-beta)=cosalpha cosbeta+sinalphas...

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  4. With the help of vector method, prove that,cosA=(b^2+c^2-a^2)/(2bc)

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  5. Prove that, in any triangle ABC, cos B=(c^2+a^2-b^2)/(2ca).

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  6. Find vecaxxvecb, if veca=2hati+hatj+3hatk and vecb=3hati+5hatj-2hatk

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  7. Find |vecaxxvecb|, if veca=3hati+4hatjand vecb=hati-hatj+hatk

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  8. Find the unit vector perpendicular to the vector veca=-hati-2hatj+3h...

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  9. Find the unit vector perpendicular to the vector veca=4hati-3hatj-ha...

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  10. Using vector, prove that sin(A+B)=sinAcosB+cosAsinB

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  11. Find the area of a parallelogram whose adjacent sides are : 3hati-4h...

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  12. Find the area of a parallelogram whose adjacent sides are : 3hati+ha...

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  13. Find the area of parallelogram whose adjacent sides are given by vecto...

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  14. If veca+vecb+vecc=vec0, show that vecaxxvecb=veccxxveca. Interpret the...

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  15. veca=hati-2hatj+3hatk and vecb=2hati+3hatj-5hatk find vecaxxvecb and v...

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  16. Find the angle between two vectors veca and vecb with magnitudes sqrt3...

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  17. The magnitude of the vector 2hati-6hatj-3hatk is :

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  18. Show that the three points with position vectors -2hati+3hatj+5hatk,ha...

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  19. The value of lambda for which the vectors veca=2hati+lambdahatj+hatk ...

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  20. Let veca=4hati+5hatj-hatk,vecb=hati-4hatj+5hatk and vecc=3hati+hatj-ha...

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