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Show that (vecaxxvecb)^2 = a^2b^2 - (vec...

Show that `(vecaxxvecb)^2 = a^2b^2 - (veca.vecb)^2`.

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Prove that (veca.vecb)^2=a^2b^2-(veca xx vecb)^2

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Show that (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb) . Interpret this result geometrically.

Prove that |veca xx vecb|^(2) = abs(veca)^(2)abs(vecb)^(2) - (veca * vecb)^(2)

If veca, vecb and vecc mutually perpendiculars, show that [veca.(vecbxxvecc)]^2 = a^2b^2c^2

Find veca*(vecaxxvecb).

If two vectors veca and vecb are such that |veca| = 3, |vecb| = 2 and veca.vecb = 6, find |veca+vecb| and |veca-vecb| .

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ARIHANT PUBLICATION-VECTOR ALGEBRA -Odisha Bureau.s Textbook Solutions (Exercise 12(c))
  1. Let a = 2hat(i) + hat(j), b = -hat(i) + 3hat(k) and c = hat(i) + 2hat(...

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  2. Let a = 2hat(i) + hat(j), b = -hat(i) + 3hat(k) and c = hat(i) + 2hat(...

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  3. Find the unit vectors perpendicular to the vectors. hati, hatk

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  4. Find the unit vector perpendicular to the vectors hat(i) + hat(j), h...

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  5. Find the unit vector perpendicular to the vectors 2hat(i) + 3hat(k),...

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  6. Find the unit vector perpendicular to the vectors 2hat(i) - 3hat(k),...

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  7. Determine the area of parallelogram whose adjacent sides are the vecto...

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  8. Determine the area of parallelogram whose adjacent sides are the vecto...

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  9. Determine the area of parallelogram whose adjacent sides are the vecto...

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  10. Determine the area of parallelogram whose adjacent sides are the vecto...

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  11. Calculate the area of the triangle ABC (by vector method) where A(1,2,...

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  12. Calculate the area of the triangle ABC (by vector method) where A(1,1,...

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  13. Determine the sine of the angle between the vectors 5hati-3hatj, 3hati...

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  14. Determine the sine of the angle between the vectors hat-3hatj+hatk, ha...

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  15. Show that (vecaxxvecb)^2 = a^2b^2 - (veca.vecb)^2.

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  16. If vecaxxvecb = vecbxxvecc ne vec0, prove that veca+vecc = mvecb, wher...

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  17. If a = 2hat(i) + hat(j) - hat(k), b = -hat(i) + 2hat(j) - 4hat(k) , c ...

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  18. If a = 3hat(i) + hat(j) + 2hat(k), b = 2hat(i) - 3hat(j) + 4hat(k), th...

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  19. Find the area of the parallelogram whose diagonals are vectors 3hati+h...

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  20. Show that (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb). Interpret this res...

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