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The projection vector of veca" on "vecb ...

The projection vector of `veca" on "vecb` is

A

`((veca.vecb)/(|vecb|))vecb`

B

`(veca.vecb)/(|vecb|)`

C

`(veca.vecb)/(|veca|)`

D

`((veca.vecb)/(|vecb|^(2)))hatb`

Text Solution

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The correct Answer is:
D
Projection vector of `veca" on "vecb` is given by `=veca.vecb)/(|vecb|)hatb=(veca.(vecb)/(|vecb|^2)) vecb`
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Write the projection of vector veca" on "vecb .

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If vecb ne 0 , then every vector veca can be written in a unique manner as the sum of a vector veca_(p) parallel to vecb and a vector veca_(q) perpendicular to vecb . If veca is parallel to vecb then veca_(q) =0 and veca_(q)=veca . The vector veca_(p) is called the projection of veca on vecb and is denoted by proj vecb(veca) . Since proj vecb(veca) is parallel to vecb , it is a scalar multiple of the vector in the direction of vecb i.e., proj vecb(veca)=lambdavecUvecb" " (vecUvecb=(vecb)/(|vecb|)) The scalar lambda is called the componennt of veca in the direction of vecb and is denoted by comp vecb(veca) . In fact proj vecb(veca)=(veca.vecUvecb)vecUvecb and comp vecb(veca)=veca.vecUvecb . If veca=-2hati+hatj+hatk and vecb=4hati-3hatj+hatk then proj vecb(veca) is

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Let veca, vecb and vecc be three vectors such that |veca|=2, |vecb|=1 and |vecc|=3. If the projection of vecb along veca is double of the projection of vecc along veca and vecb, vecc are perpendicular to each other, then the value of (|veca-vecb+2vecc|^(2))/(2) is equal to

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NCERT EXEMPLAR ENGLISH-VECTOR ALGEBRA-OBJECTIVE TPYE QUESTIONS
  1. For any vector veca the value of (vecaxxhati)^2+(vecaxxhatj)^2+(vecaxx...

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  2. If |veca|=10,|vecb|=2andveca.vecb=12, then the value of |vecaxxvecb| i...

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  3. The vectors lamdahati+hatj+2hatk,hati+lamdahatj-hatkand2hati-hatj+lamd...

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  4. If veca,vecbandvecc are unit vectors such that veca+vecb+vecc=0, then ...

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  5. The projection vector of veca" on "vecb is

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  6. If veca,vecbandvecc are three vectors such that veca+vecb+vecc=0and|ve...

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  7. If |veca|=4and-3lelamdale2, then the range of |lamdaveca| is

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  8. The number of vectors of unit length perpendicular to the vectors veca...

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  9. The vector veca+vecb bisects the angle between the non-collinear vecto...

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  10. If vecr.veca=0,vecr.vecb=0andvecr.vecc=0 for some non-zero vector vecr...

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  11. The vectors veca=3hati-2hatj+2hatkandvecb=-hati-2hatk are the adjacent...

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  12. The values of k, for which |k" "veca|lt|veca| andkveca+(1)/(2)veca is ...

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  13. The value of the expression |vecaxxvecb|^(2)+(veca.vecb)^(2) is….. .

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  14. If |vecaxxvecb|^(2)+|veca.vecb|^(2)=144and|veca|=4,"then "|vecb| is eq...

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  15. If veca is any non-zero vector, then (veca.hati)hati+(veca.hatj)hatj+(...

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  16. State true or false: If |veca|=|vecb|, then necessarily it implies vec...

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  17. State true or false: Position vector of a point vecP is a vector whose...

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  18. State true or false: If |veca+vecb|=|veca-vecb|, then the vectors veca...

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  19. The formula (veca+vecb)^(2)=vec(a^(2))+vec(b^(2))+2vecaxxvecb is valid...

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  20. State true or false: If vecaandvecb are adjacent sides of a rhombus, t...

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