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

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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

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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.

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VMC MODULES ENGLISH-VECTORS -JEE ADVANCED (ARCHIVE) (TRUE/ FALSE)
  1. The projection vector of veca" on "vecb is

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  2. Sate true/false. The points with position vectors veca + vecb, veca-ve...

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  3. Let vecA, vecB and vecC be unit vectors such that vecA.vecB = vecA.vec...

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  4. for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc...

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  5. If vecX.vecA=0, vecX.vecB=0,vecX.vecC=0 for some non-zero vector, vecX...

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  6. find three- dimensional vectors, vecv1, vecv2 and vecv3" satisfying "...

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  7. about to only mathematics

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  8. In a triangle A B C ,Da n dE are points on B Ca n dA C , respectivley,...

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  9. Determine the value of c so that for all real x , vectors c x hat i-6 ...

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  10. about to only mathematics

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  11. Let OACB be a parallelogram with O at the origin and OC a diagonal. Le...

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  12. Let vec A(t) = f1(t) hat i + f2(t) hat j and vec B(t) = g(t)hat i+g2(...

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  13. If veca, vecb, vecc and vecd ar distinct vectors such that veca xx v...

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  14. For any two vectors vecu and vecv prove that (1+|vecu|^2)(1+|vecv|^2) ...

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  15. A , B , Ca n dD are any four points in the space, then prove that |...

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  16. about to only mathematics

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  17. vecu, vecv and vecw are three nono-coplanar unit vectors and alpha, be...

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  18. about to only mathematics

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  19. Let vecu and vecv be unit vectors. If vecw is a vector such that vecw+...

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  20. The position vectors of the point A, B, C and D are 3hati-2hatj -hatk,...

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  21. If vecA , vecB and vecC are vectors such that |vecB| = |vecC| prove th...

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