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

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

A

`veca * hatb`

B

`veca - vecb`

C

`vecb * veca `

D

`hata * hatb`

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The correct Answer is:
a
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Write the projection of vector veca" on "vecb .

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=-2hatj+hatj+hatk and vecb=4hati-3hatj+hatk then proj vecb(veca) is

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

Let |A|=1, |vecb|=4 and veca xxvecr +vecb=vecr . If the projection of vecr along veca is 2, then the projection of vecr along vecb is

Given two vectors veca=2hati-3hatj+6hatk, vecb=-2hati+2hatj-hatk and lambda=("the projection of "veca on vecb)/("the projection of " vecb on veca) , then the value of lambda is

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

What is the projection of vecA on vecB ?

What is the projection of vecA on vecB ?

If vecA= 2hati-2hatj-hatk and vecB= hati+hatj , then : (a) Find angle between vecA and vecB . (b) Find the projection of resultant vector of vecA and vecB on x-axis.

If veca,vecb and vecc are three non-coplanar vectors then the length of projection of vector veca in the plane of the vectors vecb and vecc may be given by

ICSE-COMPETITION CARE UNIT-VECTORS AND SCALARS [Selected from Previoius Years Engg. & Med. & IIT Exam Qns]
  1. Two vectors of equal magnitudes having a sum of resultant equal to eit...

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  2. The angle between veca xx vecb and vecb xx veca is

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  3. If the sum of two unit vectors is a unit vector, then the magnitude of...

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  4. If hatn is a unit vector in the direction of the vector vecA, then

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  5. If vec(A)=vec(B)+vec(C ), and the magnitudes of vec(A),vec(B),vec(C ) ...

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  6. The maximum number of components into which a vector can be resolved i...

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  7. The minimum number of vectors of equal magnitude needed to produce zer...

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  8. Given that veca + vecb = veca-vecb,. This can be true when

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  9. If veca * vecb = |veca xx vecb|, then this angle between veca and vecb...

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

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  11. The angle between two vectors veca and vecb is pi//2. Then |hata xx ha...

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  12. Given that veca * vecb = 0 and veca xx vecc = 0 Then the angle between...

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  13. There are n coplanar vectors each of magnitude m and each vector is in...

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  14. Given that veca and vecb are two non zero vectors, then the value of (...

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  15. The linear velocity of rotating body is given by vecv = vecomega xx ve...

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  16. The position vectors os a particle is r=(acosomegat)hati+(asinomegat)h...

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  17. The length of the sum of the vectors veca = 3hati and b = 4hatj is

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  18. If 0.5hati + 0.8hatj + chatk is aunit vector then c is

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  19. The resultant of three vectors 1,2, and 3 units whose directions are t...

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  20. If the angle between the vector vecA and vecB is theta , the value of ...

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