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If `| vec a|=| vec b|,\ t h e n\ ( vec a+ vec b)dot( vec a- vec b)=` a. positive b. negative c. `0` d. none of these

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To solve the problem, we need to evaluate the expression \((\vec{a} + \vec{b}) \cdot (\vec{a} - \vec{b})\) given that \(|\vec{a}| = |\vec{b}|\). ### Step-by-Step Solution: 1. **Write the expression:** \[ (\vec{a} + \vec{b}) \cdot (\vec{a} - \vec{b}) \] ...
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If vec a ,\ vec b ,\ vec c are three non-zero vectors, no two f thich are collinear and the vector vec a+ vec b is collinear with vec c ,\ vec b+ vec c is collinear with vec a ,\ t h e n\ vec a+ vec b+ vec c= a. vec a b. vec b c. vec c d. none of these

If vec adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then vec b= vec c b. vec b=0 c. vec b+ vec c=0 d. none of these

Distance of the point P( vec p) from the line vec r= vec a+lambda vec b is a. |( vec a- vec p)+((( vec p- vec a)dot vec b) vec b)/(| vec b|^2)| b. |( vec b- vec p)+((( vec p- vec a)dot vec b) vec b)/(| vec b|^2)| c. |( vec a- vec p)+((( vec p- vec b)dot vec b) vec b)/(| vec b|^2)| d. none of these

If vec a_|_ vec b , then vector vec v in terms of vec aa n d vec b satisfying the equation s vec vdot vec a=0a n d vec vdot vec b=1a n d[ vec v vec a vec b]=1 is vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^2) b. vec b/(| vec b|^)+( vec axx vec b)/(| vec axx vec b|^2) c. vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^) d. none of these

If vec a and vec b are orthogonal unit vectors, then for a vector vec r noncoplanar with vec a and vec b , vector rxxa is equal to a. [ vec r vec a vec b] vec b-( vec r. vec b)( vec bxx vec a) b. [ vec r vec a vec b]( vec a+ vec b) c. [ vec r vec a vec b] vec a-( vec r. vec a) vec axx vec b d. none of these

The vector component of vec b perpendicular to vec a is ( vec bdot vec c) vec a b. ( vec axx( vec bxx vec a))/(| vec a|^2) c. vec axx( vec bxx vec a) d. none of these

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]

If vec x+ vec cxx vec y= vec aa n d vec y+ vec cxx vec x= vec b ,w h e r e vec c is a nonzero vector, then which of the following is not correct? vec x=( vec bxx vec c+ vec a+( vec cdot vec a) vec c)/(1+ vec cdot vec c) b. vec x=( vec cxx vec b+ vec b+( vec cdot vec a) vec c)/(1+ vec cdot vec c) c. vec y=( vec axx vec c+ vec b+( vec cdot vec b) vec c)/(1+ vec cdot vec c) d. none of these

For non-zero vectors vec a , vec b ,a n d vec c ,|( vec axx vec b)dot vec c|=| vec a|| vec b|| vec c| holds if and only if a. vec a* vec b=0, vec b* vec c=0 b. vec b* vec c=0, vec c* vec a=0 c. vec c* vec a=0, vec a* vec b=0 d. vec a* vec b=0, vec b* vec c=0, vec c* vec a=0

[vec a, vec b + vec c, vec d] = [vec a, vec b, vec d] + [vec a, vec c, vec d]

RD SHARMA-SCALAR OR DOT PRODUCT-Solved Examples And Exercises
  1. If vec a\ a n d\ vec b are unit vectors, then which of the following...

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  2. If the vectors hat i-2x hat j+3y hat k\ a n d\ hat i+2x hat j-3y hat...

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  3. The vector component of vec b perpendicular to vec a is ( vec bdot v...

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  4. The length of the longer diagonal of the parallelogram constructed o...

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  5. If vec a is a non zero vector a magnitude ' a^(prime)\ a n d\ lambda ...

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  6. If theta is the angle between two vectors vec a\ a n d\ vec b ,\ t h...

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  7. The values of x for which the angle between vec a=2x^2\ hat i+4x hat...

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  8. If vec a ,\ vec b ,\ vec c are any time mutually perpendicular vect...

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  9. If the vectors 3 hat i+lambda hat j+ hat k\ a n d\ 2 hat i- hat j+8 ha...

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  10. The projection of the vector hat i+ hat j+ hat k along the vector ...

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  11. The vectors 2 hat i+3 hat j-4 hat k\ a n d\ a hat i=b hat j+c hat k ar...

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  12. If | vec a|=| vec b|,\ t h e n\ ( vec a+ vec b)dot( vec a- vec b)= a....

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  13. If vec a\ a n d\ vec b are unit vectos inclined at an angle theta th...

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  14. If vec a\ a n d\ vec b are unit vectorts, then the greatest value fo...

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  15. If the angle between the vectors x hat i+3 hat j-7 hat k\ a n d\ x hat...

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  16. If \ vec a\ a n d\ vec b are two unit vectors inclined at an angle t...

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  17. Let vec a ,\ vec b ,\ vec c be three unit vectors such that | vec a...

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  18. The orthogonal projection of vec a\ on\ vec b is (( vec adot vec b) ...

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  19. If theta is an acute angle and the vector (sintheta) hat i+(costheta)...

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  20. If vec a\ a n d\ vec b be two unit vectors and theta is the angle be...

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