Let ` vec aa n d vec b` be two non-zero perpendicular vectors. A vecrtor ` vec x` satisfying the equation ` vec x xx vec b= vec a` is `vecx= beta vecb-1/|b|^2 vecaxx vecb` then `beta` can be

If vec b is not perpendicular to vec c , then find the vector vec r satisfying the equation vec rxx vec b= vec axx vec b and vec r. vec c=0.

Let vec aa n d vec b be two non-collinear unit vector. If vec u= vec a-( vec adot vec b) vec ba n d vec v= vec axx vec b ,t h e n| vec v| is a. | vec u| b. | vec u|+| vec udot vec a| c. | vec u|+| vec udot vec b| d. | vec u|+ hat udot| vec a+ vec b|

Let vec a , vec b ,a n d vec c be non-coplanar vectors and let the equation vec a^' , vec b^' , vec c ' are reciprocal system of vector vec a , vec b , vec c , then prove that vec axx vec a^'+ vec bxx vec b^'+ vec cxx vec c ' is a null vector.

vec aa n d vec b are two unit vectors that are mutually perpendicular. A unit vector that is equally inclined to vec a , vec ba n d vec axx vec b is a. 1/(sqrt(2))( vec a+ vec b+ vec axx vec b) b. 1/2( vec axx vec b+ vec a+ vec b) c. 1/(sqrt(3))( vec a+ vec b+ vec axx vec b) d. 1/3( vec a+ vec b+ vec axx vec b)

If vec a \ a n d \ vec b are two non-collinear unit vector, and ∣ ​ veca + vecb ∣ ​ = 3 ​ then (2 veca −5 vecb ).(3 veca + vecb ) =

If vec a , vec ba n d vec c are three mutually perpendicular vectors, then the vector which is equally inclined to these vectors is vec a+ vec b+ vec c b. vec a/(| vec a|)+ vec b/(| vec b|)+ vec c/(| vec c|) c. vec a/(| vec a|^2)+ vec b/(| vec b|^2)+ vec c/(| vec c|^2) d. | vec a| vec a-| vec b| vec b+| vec c| vec c

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 a. 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 aa n d vec b are two vectors and angle between them is theta, then | vec axx vec b|^2+( vec adot vec b)^2=| vec a|^2| vec b|^2 | vec axx vec b|=( vec adot vec b),iftheta=pi//4 vec axx vec b=( vec adot vec b) hat n ,(w h e r e hat n is unit vector, ) if theta=pi//4 ( vec axx vec b)dot( vec a+ vec b)=0

Let vec a and vec b be unit vectors such that | vec a+ vec b|=sqrt(3) . Then find the value of (2 vec a+5 vec b).((3 vec a+ vec b+ vec axx vec b))dot

If c is a given non-zero scalar, and vec A and vec(B) are given non-zero vector such that vec A_|_ vecB , then find vector vec X which satisfies the equation vec A . vec X =c and vec Axx vec X= vec Bdot