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

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

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If veca+vecb+vecc=vec0 , show that vecaxxvecb=vecbxxvecc=veccxxveca .

If veca,vecb,vecc are mutually perpendicular unit vectors and vecaxxvecb=vecc , show that vecb=veccxxveca and veca=vecbxxvecc .

veca =1/sqrt(10)(3hati + hatk) and vecb =1/7(2hati +3hatj-6hatk) , then the value of (2veca-vecb).[(vecaxxvecb)xx(veca+2vecb)] is:

Prove that {(vecb+vecc)xx(vecc+veca)}.(veca+vecb)=2[veca,vecb,vecc]

Let the vectors veca, vecb, vecc be given as veca_1hati + veca_2hatj + veca_3hatk, vecb_1hati + vecb_2hatj + vecb_3hatk, vecc_1hati+vecc_2hatj + vecc_3hatk . Then show that vecaxx(vecb+vecc) = vecaxxvecb + vecaxxvecc

The formula (veca+vecb)^(2)=veca^(2)+vecb^(2)+2vecaxxvecb is valid for non zero vectors veca and vecb .

Prove that veca*((vecb+vecc)xx(veca+vecb+vecc))=0 .

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

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

Show that veca*(vecaxxvecb)=0 for any pair veca,vecb of vectors.

MODERN PUBLICATION-VECTORS-Exercise
  1. Show that |vecaxxvecb|=sqrt(vec(a^2)vec(b^2)-(veca*vecb)^2).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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