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Prove that the unit vcetor perpendicular...

Prove that the unit vcetor perpendicular to each of the vcetors `2hati-hatj+hatk` and `3hati+4hatj-hatk` is : `(-3hati+5hatj+11hatk)/(sqrt(155))` and that the sine of the angle between them is `sqrt(155/156)`.

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MODERN PUBLICATION-VECTORS-Exercise
  1. If veca=2hati+sqrt3hatj+3hatk and vecb=3hati+2hatj-2sqrt3hatk, then : ...

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  2. If a unit vector veca, makes angles pi/3with hati, pi/4wih hatj and...

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  3. Prove that the unit vcetor perpendicular to each of the vcetors 2hati-...

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  4. Show that the three points veca-2vecb+3vecc, 2veca+3vecb-4vecc and -7v...

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  5. With help of vectors find the area of the triangle with vertices A(2,3...

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  6. Find, with help of vectors, the area of the triangle with vertices : A...

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  7. Find the area of triangle with vertices (1,2,4),(3,1,-2)and(4,3,1).

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  8. Find the value of 'x' if the area of triangle is 35 square cm. With ve...

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  9. If veca,vecb,vecc are any three vectors then prove that. vecaxx(vecb...

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  10. If veca,vecb,vecc are three vectors such that vecaxxvecb=vecc,vecbxxve...

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  11. If veca,vecb,vecc are mutually perpendicular unit vectors and vecaxxve...

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  12. If veca=hati+4hatj+2hatk , vecb=3hati-2hatj+7hatk and vecc=2hati-hatj+...

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  13. If vecaxxvecb=vecbxxvecc ne vec0, show that veca+vecc=vec(mb) m being ...

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  14. Prove that |vecaxxvecb|^2=|veca|^2|vecb|^2-(veca*vecb)^2=|:[veca*veca ...

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  15. If veca,vecb,vecc are position vectors of non-collinear points A,B and...

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  16. Prove that the normal to the plane containing three point whose positi...

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  17. Find the unit vectors perpendicular to the plane ABC, where the positi...

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  18. Prove that : sin(A- B) = sin A cos B -cos A sin B.

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  19. Find the moment about (1,-1,-1) of the force 3hati+4hatj-5hatk acting ...

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  20. The force represented by 3hati+2hatk is acting through the point 5hati...

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