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` vec a , vec b` and ` vec c` are the position vectors of points `A ,B` and `C` respectively, prove that : ` vec a× vec b+ vec b× vec c+ vec c× vec a` is vector perpendicular to the plane of triangle `A B Cdot`

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RD SHARMA ENGLISH-SCALAR TRIPLE PRODUCT -All Questions
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  2. Find the value of lambda for which the four points with position vecto...

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  3. vec a , vec b and vec c are the position vectors of points A ,B and C...

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  4. Let vec a= hat i+ hat j+ hat k , vec b= hat i and hat c=c1 hat i+c2...

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  5. Find [ vec a , vec b , vec c],w h e n vec a=2 hat i-3 hat j+4 hat k , ...

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  6. Find the volume of a parallelepiped whose edges are given by -3 hat ...

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  7. If |a a^2 1+ahat3bb^2 1+b^3cc^2 1+c^3|=0 and the vectors vec A= hat i...

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  8. Evaluate 0.2^3 + 100.45^0

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  9. Simplify: [ vec a- vec b vec b- vec c vec c- vec a]

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  10. If the vectors vecalpha=a hat i+a hat j+c hat k , vecbeta= hat i+ hat...

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  11. Determine alpha such that a vector vec r is at right angles to each o...

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  12. Find the range of f(x)=sin^(-1)x+tan^(-1)x+cos^(-1)xdot

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  13. If vec a , vec b , vec c are three non-coplanar vectors, prove that [...

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  14. For any three vectors a b,c, show that vec a xx (vec b +vec c)+vec b x...

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  15. Let vec a , vec b , vec c be three non-zero vectors such that vec c ...

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  16. Let vec a , vec ba n d vec c , be non-zero non-coplanar vectors. Prov...

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  17. Find the altitude of a parallelepiped determined by the vectors ve...

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  18. Let vec a , vec b , vec c , be three non-zero vectors. If vec a .(ve...

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  19. If the vectors vecalpha=a hat i+ hat j+ hat k , vecbeta= hat i+b hat ...

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  20. If a is a non-zero real number, then prove that the vectors vecalph...

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