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

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

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Let the vectors 'veca, vecb, vecc' be given as 'a_1 hati+a_2 hatj+a_3 hatk, b_1 hati+b_2 hatj+b_3 hatk, c_1 hati+c_2 hatj+c_3 hatk', Then show that 'veca xx(vecb+vecc)=veca xx vecb+veca xx vecc'

Prove that (veca xx vecb)^2=|(veca.veca,veca.vecb),(veca.vecb,vecb.vecb)| .

Prove that (veca+vecb).(veca+vecb)=|veca|^2+|b|^2 if and only if veca,vecb are perpendicular, given veca!=vec0"and"vecb!=0 .

Prove that [ veca+vecb vecb+vecc vecc+veca]=2[veca vecb vecc]

With help of a suitable figure for any three vectors veca,vecb and vecc show that (veca+vecb)+vecc=veca+(vecb+vecc)

Find |veca| and |vecb| , if (veca+vecb) .(veca-vecb)=8 and |veca|=8|vecb|

V PUBLICATION-VECTOR ALGEBRA-QUESTION BANK
  1. Find a unit vector perpendicular to each of the vector veca+vecb, and ...

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  2. Choose the correct answer from the backet. If a unit vector hata makes...

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

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  4. Find lambdaand mu if (2overset^^i+6overset^^j+27overset^^k)xx(overset^...

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  5. Given that oversetrarra.oversetrarrb=0"and"oversetrarraxxoversetrarrb=...

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  6. Let the vectors 'veca, vecb, vecc' be given as 'a1 hati+a2 hatj+a3 hat...

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  7. If either veca=vec0"or" vecb =vec0, "then"vecaxxvecb=vec0.Is the conve...

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

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  9. Find the area of the parallelogram whose adjacent sides are determined...

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  10. Let the vectorsveca"and"vecbbe such that |veca|=3"and"|vecb|=sqrt2/3,...

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

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  12. If hati+hatj+hatk, 2 hati+5 hatj, 3 hati+2 hatj-3 hatk and hati-6 hatj...

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  13. Let veca,vecb, " and " vecc be three vectors such that |veca|=3,|vecb|...

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  14. Three vectors veca,vecb,"and" vecc satisfy the conditionveca+vecb+vecc...

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  15. Write down a unit vector in XY plane making an angle of 30^@ with the...

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

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  17. If 'veca=vecb+vecc', then is it true that '|veca|=|vecb|+|vecc| ?' Jus...

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

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  19. Find a vector of magnitude 5 units and parallel to the resultant of th...

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  20. if veca=hati+hatj+hatk, vecb=2 hati-hatj+3 hatk and vecc=hati-2 hatj+h...

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