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For any two vectors vecaandvecb , we alw...

For any two vectors `vecaandvecb` , we always have `|veca*vecb|le|veca||vecb|`(Cauchy- Schwartz inequality).

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KUMAR PRAKASHAN-VECTOR ALGEBRA -Textbook Illustrations for Practive Work
  1. Find |vec(a)-vec(b)|, if two vectors vec(a) and vec(b) are such that |...

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  2. If vec(a)is a unit vector and (vec(x)-vec(a)).(vec(x)+vec(a))=8 then f...

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  3. For any two vectors vecaandvecb , we always have |veca*vecb|le|veca||v...

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  4. For any two vectors vec(a) and vec(b), we always have |vec(a)+vec(b)|l...

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  5. Show that the points A(-2hati+3hatj+5hatk),B(hati+2hatj+3hatk)andC(7ha...

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  6. Find |vecaxxvecb|, if veca=2hati+hatj+3hatk and vecb=3hati+5hatj-2hatk

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  7. Find a unit vector perpendicualr to each of the vectors (vec(a)+vec(b)...

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  8. Find the area of atriangle having the points A(1,1,1), B (1,2,3) and C...

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

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  10. If vec(a)=2hati+hatj+3hatk,vec(b)=-hati+2hatj+hatk and vec( c )=3hati+...

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  11. Show that the vectors vec(a)=hati-2hatj+3hatk,vec(b)=-2hati+3hatj-4hat...

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  12. If the vectors vec(a)=hati+3hatj+hatk,vec(b)=2hati-hatj-hatk and vec( ...

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  13. If 4hati+5hatj+hatk,-(hatj+hatk),3hati+9hatj+4hatk and 4(-hati+hatj+ha...

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  14. Prove that [vec(a)+vec(b), vec(b)+vec( c ), vec( c )+vec(a)]=2[vec(a)...

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  15. Prove that [vec(a),vec(b),vec( c )+vec(d)]=[vec(a),vec(b),vec( c )]+[v...

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  16. Write all the unit vectors in XY-plane.

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

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  18. Let vec(a),vec(b) and vec( c ) be three vectors such that |vec(a)|=3,|...

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  19. Three vectors vec(a),vec(b) and vec( c ) satisfy the condition vec(a...

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

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