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If vecaxxvecb=veccxxvecdand vecaxxvecc=v...

If `vecaxxvecb=veccxxvecdand vecaxxvecc=vecbxxvecd`, show that `veca-vecd` is parallel to `vecb-vecc`, provided `vecanevecd` and `vecbnevecc`

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

If [vecaxxvecb vecbxxvecc veccxxveca]=lambda[veca vecb vecc]^2 , then lambda is equal to :

If vecc is normal to veca and vecb , show that vecc is normal to veca+vecb and veca-vecb .

If veca+vecb+vecc=vec0 and |veca|=3,|vecb|=5,|vecc|=7 , show that the angle between veca and vecb is 60^(@)

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

If (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc), Where veca, vecb and vecc and any three vectors such that veca.vecb=0,vecb.vecc=0, then veca and vecc are

If veca+5vecb=vecc and veca -7 vecb =2vecc , then show that veca has the same direction as that of vecc and opposite direction to that of vecb .

If veca+vecb+vecc=vec0 , show that vecaxxvecb=veccxxveca . Interpret the result geometrically.

If veca*vecbxxvec=0 and vec(a')=(vecbxxvecc)/(veca*vecbxxvecc), vec(b')=(veccxxveca)/(veca*vecbxxvecc),vec(c')=(vecaxxvecb)/(veca*vecbxxvecc) , show that : veca*vec(a')+vecb*vec(b')+vecc*vec(c')=3 .

If veca,vecb,vecc are three vectors such that vecaxxvecb=vecc,vecbxxvecc=veca , prove that veca,vecb,vecc are mutually at right angles and |vecb|=1,|vecc|=|veca| .

ACCURATE PUBLICATION-VECTOR ALGEBRA-QUESTIONS CARRYING 2 MARKS
  1. Dot product of a vector with vectors hati-hatj+hatk,2hatk+hatj+3hatk a...

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  2. If veca+vecb+vecc=vec0 and |veca|=3,|vecb|=5,|vecc|=7, show that the a...

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  3. If veca, vecb, vecc are mutually perpendicular vectors of equal magnit...

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  4. If veca, vecb, vecc are mutually perpendicular vectors of equal magnit...

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  5. If veca,vecb,vecc are three vectors such that : |veca|=5,|vecb|=12 and...

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  6. If with reference to the right handed system of mutually perpendicular...

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  7. Using vectors, prove that a parallelogram whose diagonals are equal is...

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  8. For any vector veca the value of (vecaxxhati)^(2)+(vecaxxhatj)^(2)+(ve...

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  9. Find a unit vector perpendicular to the plane of triangle ABC where th...

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  10. Find a unit vector perpendicular to each of the vectors (veca+vecb) an...

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  11. Find a vector of magnitude sqrt(171), which is perpendicular to both o...

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  12. Find a vector of magnitude 5 units, perpendicular to each of the vecto...

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  13. Find the area of a parallelogram whose adjacent sides are represented ...

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  14. If veca=2hati-3hatj+hatk, vecb=hati+hatk, vecc=2hatj-hatk are three ve...

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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. Using vectors find the area of the triange ABC with vertices A(1,2,3),...

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  17. If vecaxxvecb=veccxxvecdand vecaxxvecc=vecbxxvecd, show that veca-vecd...

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  18. If veca=hati+hatj+hatk and vecb=hatj-hatk, find a vector vecc such tha...

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  19. Let veca=hati+4hatj+2hatk,vecb=3hati-2hatj+7hatk and vecc=2hati-hatj+4...

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  20. If vecr=xhati+yhatj+zhatk, find : (vecrxxhati)*(vecrxxhatj)+xy.

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