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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| .

BETTER CHOICE PUBLICATION-VECTOR ALGEBRA -ASSIGNMENT MOST IMPORTANT QUESTIONS FOR PRACTICE (SECTION V)
  1. If veca=hati+hatj-3hatk and vecb=hatj+2hatk find |2vecb+veca|

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  2. Find a unit vector perpendicular to both veca and vecb if veca=4hati...

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  3. Find a unit vector perpendicular to both veca and vecb if veca=3hati...

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  4. Find a unit vector perpendicular to both veca and vecb if veca=4hati...

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  5. Find the unit vector perpendicular to veca+vecb and veca-vecb if vec...

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  6. Find a vector of magnitude 5 units, perpendicular to both veca+vecb an...

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  7. Find the value of p for which veca=3hati+2hatj+12hatk and vecb=hati+ph...

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  8. Find the value of lambda if two vectors 2hati+3hatj-hatk and 4hati+6ha...

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  9. Find the area of a parallelogram whose adjacent sides are given by v...

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  10. Find the area of a parallelogram whose adjacent sides are given by v...

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  11. Find the area of a parallelogram whose adjacent sides are given by v...

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  12. Find the area of a parallelogram whose adjacent sides are given by v...

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  13. Find the area of the triangle (using vectors) with vertices A(3,-1,2),...

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

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  15. Find the sine of the angle between the vectors veca=2hati-3hatj+4hatk,...

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  16. If veca and vecb are any two vectors, prove that (vecaxxvecb)^(2)=|vec...

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  17. If |veca|=5,|vecb|=4 and veca.vecb=16 find |vecaxxvecb|.

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

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

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

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