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The vector component of vec b perpendic...

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

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To find the vector component of \(\vec{b}\) that is perpendicular to \(\vec{a}\), we can follow these steps: ### Step 1: Understand the components of vector \(\vec{b}\) A vector can be decomposed into two components: one that is parallel to another vector and one that is perpendicular to it. In this case, we want to find the component of \(\vec{b}\) that is perpendicular to \(\vec{a}\). ### Step 2: Find the parallel component of \(\vec{b}\) The component of \(\vec{b}\) that is parallel to \(\vec{a}\) can be calculated using the projection formula: \[ ...
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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 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

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

Let vec a , vec b , a n d vec c be three non-coplanar vectors and vec d be a non-zero vector, which is perpendicular to ( vec a+ vec b+ vec c)dot Now vec d=( vec axx vec b)sinx+( vec bxx vec c)cosy+2( vec cxx vec a)dotT h e n a.( vec ddot( vec a+ vec b))/([ vec a vec b vec c])=2 b.( vec ddot( vec a+ vec b))/([ vec a vec b vec c])=-2 c. minimum value of x^2+y^2 is pi^2//4 d. minimum value of x^2+y^2 is 5pi^2//4

If vec a , vec ba n d vec c are three non coplanar vectors, then prove that vec d=( vec adot vec d)/([ vec a vec b vec c])( vec bxx vec c)+( vec bdot vec d)/([ vec a vec b vec c])( vec cxx vec a)+( vec cdot vec d)/([ vec a vec b vec c])( vec axx vec b)

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

Let vec a , vec ba n d vec c be three non-coplanar vectors and vec p , vec qa n d vec r the vectors defined by the relation vec p=( vec bxx vec c)/([ vec a vec b vec c]), vec q=( vec cxx vec a)/([ vec a vec b vec c])a n d vec r=( vec axx vec b)/([ vec a vec b vec c])dot Then the value of the expression ( vec a+ vec b)dot vec p+( vec b+ vec c)dot vec q+( vec c+ vec a)dot vec r is a. 0 b. 1 c. 2 d. 3

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

If vec rdot vec a= vec rdot vec b= vec rdot vec c=1/2 or some nonzero vector vec r , then the area of the triangle whose vertices are A( vec a),B( vec b)a n dC( vec c)i s( vec a , vec b , vec c are non-coplanar) |[ vec a vec b vec c]| b. | vec r| c. |[ vec a vec b vec c] vec r| d. none of these

Vectors vec Aa n d vec B satisfying the vector equation vec A+ vec B= vec a , vec Axx vec B= vec ba n d vec A*vec a=1,w h e r e vec aa n d vec b are given vectors, are a. vec A=(( vec axx vec b)- vec a)/(a^2) b. vec B=(( vec bxx vec a)+ vec a(a^2-1))/(a^2) c. vec A=(( vec axx vec b)+ vec a)/(a^2) d. vec B=(( vec bxx vec a)- vec a(a^2-1))/(a^2)

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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