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

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

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

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

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 .

MODERN PUBLICATION-VECTORS-Exercise
  1. Find a unit vector perpendicular to each of the vector veca + vecb and...

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

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

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

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

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  6. Let the vectors veca,vecb,vecc be given as : a1hati+a2hatj+a3hatk,b1ha...

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  7. If either veca = vec0or vecb = vec0 then vecaxxvecb= vec0. Is the con...

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  8. Find the area of the triangle with vertices A(1,12), B(2,3,5), C(1,5,5...

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  9. Determine the area of a parallelogram whose adjacent sides are represe...

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  10. Let the vectors veca and vecb be such that |veca| = 3 and |vecb| = sqr...

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  11. Area of a rectangle having vertices A, B, C and D with position vector...

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  12. Write down a unit vector in XY-plane, making an angle of 30^o with the...

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  13. Find the scalar components and magnitude of the vector joining the poi...

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  14. A girl walks 4 km towards west, then she walks 3 km in a direction 30^...

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  15. If veca = vecb + vecc, then is it true that |veca| = |vecb| + |vecc|?...

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  16. Find the value of x for which x(hati + hatj + hatk) is a unit vector.

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  17. Find a vector of magnitude 5 units, and parallel to the resultant of t...

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  18. If veca=hati+hatj+hatk,vecb=2hati-hatj+3hatk,vecc=hati-2hatj+hatk, the...

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  19. Show that the points A(1,-2,-8), B(5,0,-2) and C(11,3,7) are collinear...

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  20. Find the position vector of a point R which divides the line joining t...

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