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Given veca=1/7(2hati+3hatj+6hatk), vecb...

Given `veca=1/7(2hati+3hatj+6hatk)`, `vecb=1/7(3hati-6hatj+2hatk)` , `vecc=1/7(6hati+2hatj-3hatk)` , `hati,hatj,hatk` being a right handed orthogonal system of unit vectors in space. Show that `veca,vecb,vecc` is also another such system.

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MODERN PUBLICATION-VECTORS-Exercise
  1. Prove that the quadrilateral obtained by joining mid-points of adjacen...

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  2. Prove that 1/2 vec(AC)xxvec(BD) represents the vector area of the plan...

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  3. Given veca=1/7(2hati+3hatj+6hatk), vecb=1/7(3hati-6hatj+2hatk) , ve...

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  4. If veca,vecb,vecc are coplanar then show that veca+vecb, vecb+vecc and...

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  5. Are vectors veca and -veca collinear ?

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  6. Write two different vectors having same magnitude.

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  7. What is the unit vector in the direction of veca=veci+vecj+2veck?

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  8. What is the position vector of the mid-point of the line segment joini...

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  9. The scalar product of two given vectors veca and vecb having angle 'th...

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  10. For mutually perpendicularl unit vectors hati,hatj,hatk, we have : hat...

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  11. What is the value of : hati*(hatjxxhatk)+hatj.(hatkxxhati)+hatk.(hatjx...

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  12. If |veca*vecb|=|vecaxxvecb|,then angle between veca and vecb is :

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  13. Classify the following as vector as scalar : veca*vecb,[vecavecbvecc],...

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  14. What is [vecavecbvecc] when veca,vecb,vecc are coplanar ?

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  15. In /\ABC, which of the following is not true ?

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  16. If veca and vecb are two collinear vectors, then which of the followin...

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  17. If veca is a nonzero vector of magnitude 'a' and lambda a nonzero s...

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  18. Let lambda be any non-zero scalar. Then for what possible values of x,...

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  19. Let the vectors veca and vecb be such that |veca|=3 and |vecb|=(sqrt2)...

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  20. Area of a rectangle having vertices : A(-hati+1/2 hatj+4hatk),B(hati+1...

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