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Prove that {(vecb+vecc)xx(vecc+veca)}.(v...

Prove that `{(vecb+vecc)xx(vecc+veca)}.(veca+vecb)=2[veca,vecb,vecc]`

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Prove that veca*((vecb+vecc)xx(veca+vecb+vecc))=0 .

Simplify : {(vecb-vecc)xx(vecc-veca)}odot(veca-vecb)

Simplify : {(vecb+vecc)xx(vecc+veca))}odot(veca+vecb)

prove that : [veca+vecb,vecb+vecc,vecc+veca]=2[veca,vecb,vecc]

Let veca and vecc be unit vectors inclined at pi//3 with each other. If (veca xx (vecb xx vecc)). (veca xx vecc)=5 , then [vecavecbvecc] is equal to

Simplify : (vecb+vecc)*{(vecc+veca)xx(veca+vecb)} .

If veca,vecb,vecc are any three vectors then prove that. vecaxx(vecb+vecc)+vecbxx(vecc+veca)+veccxx(veca+vecb)=0

If veca and vecb are two vectors , then prove that (vecaxxvecb)^(2)=|{:(veca.veca" ",veca.vecb),(vecb.veca" ",vecb.vecb):}|

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| .

Prove that |vecaxxvecb|^2=|veca|^2|vecb|^2-(veca*vecb)^2=|:[veca*veca veca*vecb],[veca*vecb vecb*vecb]:| .

BETTER CHOICE PUBLICATION-VECTOR ALGEBRA -PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE (MCQ)
  1. The value of lambda for which the vectors veca=2hati+lambdahatj+hatk ...

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  2. Let veca=4hati+5hatj-hatk,vecb=hati-4hatj+5hatk and vecc=3hati+hatj-ha...

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  3. Find the scalar projection of vecb on veca where : veca=2hati-2hatj+ha...

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  4. If veca=2hati-2hatj+hatk,vecb=hati+2hatj-2hatk and vecc=2hati-hatj+4ha...

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  5. Find the area of the parallelogram whose diagonals are : veca=hati-2ha...

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  6. Find the position vector of a point R which divides the line joining t...

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  7. Find the angle between two vectors vecaand vecb with magnitudes 1 and ...

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  8. Find a vector of magnitude 19, which is perpendicular to both the vect...

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  9. Find a vector of magnitude 7 , which is perpendicular to both the vect...

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  10. Find the area of triangle with vertices (1,1,2),(2,3,5),(1,5,5).

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  11. Find the area of triangle with vertices (1,2,4),(3,1,-2)and(4,3,1).

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  12. Find |veca-vecb|, if two vectors veca and vecb are such that |veca|=2,...

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  13. If |veca|=3, |vecb|=4 and |vecc|=5 and each of them is perpendicular ...

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  14. Prove that {(vecb+vecc)xx(vecc+veca)}.(veca+vecb)=2[veca,vecb,vecc]

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  15. If vec a and vec b are unit vectors and theta is the angle between the...

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  16. For what value of 'lambda' are the following vectors coplanar? : hat...

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  17. For what value of 'lambda' are the following vectors coplanar? : hat...

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  18. veca=hati+hatj+hatk,vecb=2hati-hatj+3hatk,vecc=hati-2hatj+hatk then fi...

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

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  20. Find the value of lambda. such that given vectors 3hati+lambdahatj+5ha...

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