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The unit vector bar(a) and bar(b) are pe...

The unit vector `bar(a)` and `bar(b)` are perpendicualr to each other. The unit vector `bar( c )` makes an angle `theta` with `bar(a)` and `bar(b)`.
If `bar( c )=alpha bar(a)+beta bar(b)+gamma(bar(a)xx bar(b))` then …………

A

`alpha=2beta`

B

`gamma^(2)=1+2alpha^(2)`

C

`gamma^(2)=cos2theta`

D

`beta^(2)=(1+cos2 theta)/(2)`

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The correct Answer is:
D
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KUMAR PRAKASHAN-VECTOR ALGEBRA -Solutions of NCERT Exemplar Problems (Multiple Choice Questions (MCQs) )
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  2. bar(b)=3hatj+4hatk,bar(a)=hati+hatj. If bar(b(1)) and bar(b(2)) are co...

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  3. The unit vector bar(a) and bar(b) are perpendicualr to each other. The...

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  4. Vector bar(a)=6hati-3hatj,bar(b)=2hati-6hatj and bar( c )=-2hati+21hat...

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  5. bar(a),bar(b) and bar( c ) are unit vectors. The value of |bar(a)-bar(...

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  6. If bar(a),bar(b) and bar( c ) are perpendicualr to bar(b)+bar( c ),bar...

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  7. bar(a) and bar(b) are unit vectors. |bar(a)+bar(b)|=sqrt(3) then the v...

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  8. DeltaABC is an equilateral triangle. Its side is l. Any point P lies o...

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  9. vec(a)=2hati+hatj+hatk and vec(b)=hati-hatj-hatk are the adjacent side...

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  10. The position vectors of four points A, B, C and D in the plane are vec...

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  11. If vec(alpha)=(1)/(a)hati+(4)/(b)hatj+b hatk and vec(beta)=b hati+a ha...

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  12. The unit vectors vec(a),vec(b) and vec( c ) are not coplanar. If vec(a...

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  13. If vec(x)+vec(y)+vec(z)=0 and |vec(x)|=|vec(y)|=|vec(z)|=2 If the angl...

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  14. vec(a)=2hati-hatj+hatk,vec(b)=hati+2hatj-hatk,vec( c )=hati+hatj-2hatk...

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  15. vec(a)=hati+hatj+sqrt(2)hatk,vec(b)=b(1)hati+b(2)hatj+sqrt(2)hatk and ...

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  16. vec(a)=2hati+lambda(1)hatj+3hatk,vec(b)=4hati+(3-lambda(2))hatj+6hatk ...

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  17. squareABCD is a parallelogram vec(AB)=bar(q),vec(AD)=bar(p),angleBAC i...

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  18. The position vectors of A, B and C are 2hati-hatj+hatk,hati-3hatj-5hat...

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  19. A particle is acted upon constant forces vec(F)(1)=4hati+hatj-3hatk an...

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  20. Let vec(u),vec(v) and vec(w) be such that |vec(u)|=1,|vec(v)|=2,|vec(w...

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