Find 3-dimensional vectors `vec v_1,vec v_2,vec v_3` satisfying `vec v_1* vec v_1=4,vec v_1* vec v_2=-2,vec v_1* vec v_3=6,`
`vec v_2* vec v_2=2 , vec v_2 *vec v_3=-5,vec v_3* vec v_3=29`

If vec a , vec ba n d vec c are unit vectors satisfying | vec a- vec b|^2+| vec b- vec c|^2+| vec c- vec a|^2=9, then |2 vec a+5 vec b+5 vec c| is.

For any two vectors vec ua n d vec v prove that ( vec u. vec v)^2+| vec uxx vec v|^2=| vec u|^2| vec v|^2

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 a , vec b and vec c are three non-zero, non coplanar vector vec b_1= vec b-( vec b . vec a)/(| vec a|^2) vec a , vec c_1= vec c-( vec c . vec a)/(| vec a|^2) vec a+( vec b . vec c)/(| vec c|^2) vec b_1 , , c_2= vec c-( vec c . vec a)/(| vec a|^2) vec a-( vec b . vec c)/(| vec b_1|^2) , b_1, vec c_3= vec c-( vec c . vec a)/(| vec c|^2) vec a+( vec b . vec c)/(| vec c|^2) vec b_1 , vec c_4= vec c-( vec c . vec a)/(| vec c|^2) vec a=( vec b . vec c)/(| vec b|^2) vec b_1 then the set of orthogonal vectors is a. ( vec a , vec b_1, vec c_3) b. ( vec a , vec b_1, vec c_2) c. ( vec a , vec b_1, vec c_1) d. ( vec a , vec b_2, vec c_2)

If vec e_1, vec e_2, vec e_3a n d vec E_1, vec E_2, vec E_3 are two sets of vectors such that vec e_idot vec E_j=1,ifi=j and vec e_idot vec E_j=0a n difi!=j , then prove that [ (vec e_1, vec e_2 ,vec e_3)][ (vec E_1, vec E_2, vec E_3) ]=1.

If vec a, vec b, vec c are unit vectors satisfying the condition veca+ vec b+ vec c= 0 then show that vec a. vec b+ vec b.vec c+ vec c. vec a= -3//2 .

Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c . Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] ; then vec d equally inclined to vec a , vec b and vec c . (a) statement 1 is true but statement 2 is false. (b) statement 2 is true but statement 1 is false. (c)both the statements are true. (d) both the statements are false.

If [ vec a vec b vec c]=2, then find the value of [( vec a+2 vec b- vec c)( vec a- vec b)( vec a- vec b- vec c)]dot

Let vec u and vec v be unit vectors such that vec uxx vec v+ vec u= vec w and vec wxx vec u= vec v . Find the value of [ vec u \ vec v \ vec w] .

Let vec r be a unit vector satisfying vec rxx vec a= vec b ,w h e r e| vec a|=sqrt3a n d| vec b|=sqrt2. Then vec r =?