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The vector vecb = 3j + 4k is to be writt...

The vector `vecb = 3j + 4k` is to be written as the sum of a vector `vecb_1`, parallel to `veca = i + j`, and a vector `vecb_2`, perpendicular to `veca`, then `vecb_1`, equals

A

`3/2 (vec i + vec j)`

B

`2/3 (vec i + vec j)`

C

`(1/2 (vec i + vec j)`

D

none of these

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If the vector vecb = 3hati + 4hatk is written as the sum of a vector vecb_(1) parallel to veca = hati + hatj and a vector vecb_(2) , perpendicular to veca then vecb_(1) xx vecb_(2) is equal to:

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

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The vector (veca.vecb)vecc-(veca.vecc)vecb is perpendicular to

l veca . m vecb = lm(veca . vecb) and veca . vecb = 0 then veca and vecb are perpendicular if veca and vecb are not null vector

If veca , vecb are unit vectors such that the vector veca + 3vecb is peependicular to 7 veca - vecb and veca -4vecb is prependicular to 7 veca -2vecb then the angle between veca and vecb is

If veca , vecb are two vectors such that | (veca+vecb)=|veca| then prove that 2 veca + vecb is perpendicular to vecb.

If veca, vecb and vecc are vectors such that |veca|=3,|vecb|=4 and |vec|=5 and (veca+vecb) is perpendicular to vecc,(vecb+vecc) is perpendicular to veca and (vecc+veca) is perpendicular to vecb then |veca+vecb+vecc|= (A) 4sqrt(3) (B) 5sqrt(2) (C) 2 (D) 12

If |veca+vecb|=|veca-vecb|, (veca,vecb!=vec0) show that the vectors veca and vecb are perpendicular to each other.

A DAS GUPTA-Product of two Vectors-Exercise
  1. If |vec a|=3,|vec b|=5,|vec c|=7 and vec a+vec b+vec c=0 then angle be...

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  2. The conditions under which the vector vec P + vec Q and vec P - vec Q ...

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  3. Let vec O A- vec a , hat O B=10 vec a+2 vec ba n d vec O C= vec b ,w ...

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  4. Vector vec O A= hat i+2 hat j+2 hat k turns through a right angle ...

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  5. A vector a has components a1,a2,a3 in a right handed rectangular cart...

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  6. If vec a * vec b = vec a * vec c then

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  7. If vec(A)+vec(B)+vec(C )=0 then vec(A)xx vec(B) is

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  8. If vec a xx vec b= vec b xx vec c != vec 0 then which one is true wh...

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  9. A, B, C and D are four points in a plane with position vectors vec a,v...

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  10. If |vec a|= |vec b|= 1 and |vec a xx vec b|=1 then

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  11. The vector vecb = 3j + 4k is to be written as the sum of a vector vecb...

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  12. Let veca=2hati-hatj+hatk , vecb= hati+2hatj-hatk and vec c= hati+hatj-...

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  13. If vec a+ vec b+ vec c=0 and | vec a|=3,\ | vec b|=5 and | vec c|=7 ...

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  14. If vec(a). vec(b) = 0 and vec(a) xx vec(b) = vec(0) then which one of ...

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  15. If vec a=4 hat i+6 hat ja n d vec b=3 hat j+4 hat k , then find the c...

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  16. In each of the following, fill in the blank so that the resulting stat...

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  17. If vec(A) xx vec(B) = vec(B) xx vec(A), then the angle between A to B ...

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  18. Find a unit vector vec cif- vec i+ vec j- vec kb i s e c t st h ea ng...

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  19. If theta is the angle between the unit vectors hat a and hat b then co...

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  20. In each of the following, one or more options are correct. Choose the...

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