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Show that |vecaxxvecb|=sqrt(vec(a^2)vec(...

Show that `|vecaxxvecb|=sqrt(vec(a^2)vec(b^2)-(veca*vecb)^2)`.

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

If veca and vecb are any two vectors, prove that (vecaxxvecb)^(2)=|veca|^(2)|vecb|^(2)-(veca.vecb)^(2) It is known as Largange's indentity.

Prove that : (vecaxxvecb)^2=|\veca|^2.|\vecb|^2-(veca.vecb)^2 .

Show that (veca-vecb)xx(veca+vecb)=2(vecaxxvecb) .

Show that (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb)

Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

If vec a and vec b are any two vectors, show that |vec a xxvec b|^2= [[vec a*vec a,vec a*vec b],[vec a*vec b,vec b* vec b]] .

If |veca|=a and |vecb|=b , prove that ((veca)/(a^2)-(vecb)/(b^2))^2=((veca-vecb)/(ab))^2 .

If veca*vecb*vecc not= 0 and vec(a')=(vecbxxvecc)/(veca*vecbxxvecc), vec(b')=(veccxxveca)/(veca*vecbxxvecc),vec(c')=(vecaxxvecb)/(veca*vecbxxvecc) , show that : vec(a')*(vec(b')xxvec(c'))=1/(veca*(vecbxxvecc) .

MODERN PUBLICATION-VECTORS-Exercise
  1. Find the area of the quadrilateral whose diagonals are given by 3hat...

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  2. Show that the area of the parallelogram with diagonals veca and vecb, ...

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  3. Show that |vecaxxvecb|=sqrt(vec(a^2)vec(b^2)-(veca*vecb)^2).

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  4. Prove that |vecaxxvecb|/(veca*vecb)= tan theta, where theta is the ang...

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  5. Show that (veca-vecb)xx(veca+vecb)=2(vecaxxvecb).

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  6. Given that veca cdot vecb = 0 and vecaxxvecb = vec0. What can you conc...

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  7. Find |veca*vecb|, if |veca|=5,|vecb|=13 and |vecaxxvecb|=25.

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  8. If |veca|=13,|vecb|=5 and veca*vecb=60, then find |vecaxxvecb|.

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  9. Find lambda and mu if : (2hati+6hatj+27hatk)xx(hati+lambdahatj+muhatk)...

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  10. If veca=2hati+sqrt3hatj+3hatk and vecb=3hati+2hatj-2sqrt3hatk, then : ...

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  11. If veca=2hati+sqrt3hatj+3hatk and vecb=3hati+2hatj-2sqrt3hatk, then : ...

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  12. If veca=2hati+sqrt3hatj+3hatk and vecb=3hati+2hatj-2sqrt3hatk, then : ...

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  13. If veca=2hati+sqrt3hatj+3hatk and vecb=3hati+2hatj-2sqrt3hatk, then : ...

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

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

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

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

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

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

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

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