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Prove that |vecaxxvecb|^2=|veca|^2|vecb|...

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

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MODERN PUBLICATION-VECTORS-Exercise
  1. If veca=hati+4hatj+2hatk , vecb=3hati-2hatj+7hatk and vecc=2hati-hatj+...

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

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

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

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

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

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

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

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

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  10. Find the moment about the point hati+2hatj-hatk of a force represented...

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  11. The force represented by 5hati+hatk is acting through the point 9hati-...

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  12. A force vecF=4hati+hatk acts through point A(0,2,0). Find the moment v...

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  13. Let vecF=2hati+4hatj+3hatk at the point P with position vector hati-ha...

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  14. A force vecF=3hati+2hatj-4hatk is applied at the point (1,-1,2).Find t...

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  15. Two unlike forces of equal magnitudes hatj+2hatk and -hatj-2hatk are a...

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  16. A force of 3 units acts through the point (4,-1,7) in the direction of...

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  17. Find the moment about the point (3,4,5) of the force through the point...

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  18. The moment of the couple formed by forces 5hati+hatk and -5hati-hatk a...

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  19. Find the vector moment of the forces : hati+2hatj-3hatk: 2hati+3hatj+4...

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  20. Classify the following quantities as vector or scalar : (i) Time perio...

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