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Let A B C D be a p[arallelogram whose di...

Let `A B C D` be a p[arallelogram whose diagonals intersect at `P` and let `O` be the origin. Then prove that ` vec O A+ vec O B+ vec O C+ vec O D=4 vec O Pdot`

A

`vecOP`

B

`2vecOP`

C

`3veOP`

D

`4vecOP`

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AAKASH INSTITUTE-VECTOR ALGEBRA-ASSIGNMENT (SECTION-B)
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  2. If a and b are position vectors of A and B respectively the position v...

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  3. The points with position vectors 60hati+3hatj,40hati-8hatj, 40hati-8ha...

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  4. veca,vecb,vecc are three non-coplanar such that veca + vecb + vecc = a...

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  5. The position vector of three points are 2veca-vecb+3vecc, veca-2vecb+l...

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  6. Let a,b,c be three distinct positive real numbers. If vecp,vecq,vecr l...

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  7. Let veca and vecb are unit vectors inclined at an angle alpha to each ...

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  8. A unit vector in the xy-plane that makes an angle of pi/4 with the vec...

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  9. The vectors 2hati-lamdahatj+3lamdahatk and (1+lamda)hati-2lamdahatj+ha...

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  10. Let veca,vecb and vecc are three vectors such that |veca|=3, |vecb|=3,...

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  11. If veca=hati+hatj+hatk, vecb=4hati+3hatj+4hatk and vecc=hati+alphahatj...

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  12. Let veca=2hati=hatj+hatk, vecb=hati+2hatj-hatk and vecc=hati+hatj-2hat...

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  13. find the area of a parallelogram whose diagonals are veca=3hati+hatj-2...

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  14. If veca and vecb are two unit vectors, then the vector (veca+vecb)xx(v...

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  15. Let veca=2hati+2hatj+hatk and vecc is a vector such that |vecaxxvecc|^...

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  16. ABCD is a quadrilateral with vec(AB) = veca, vec(AD) = vecb and vec(A...

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  17. A unit vector perpendicular to the plane passing through the points w...

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  18. If veca , vecb, vecc are the position vectors of the vertices. A,B,C ...

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  19. If vecpxxvecq=vecr and vecp.vecq=c, then vecq is

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  20. If veca=hati+hatj+hatk, veca.vecb=1 and vecaxxvecb=hatj-hatk then vecb

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