` 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)`

Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

If vec a+2 vec b+3 vec c=0,t h e n vec axx vec b+ vec bxx vec c+ vec cxx vec a= 2( vec axx vec b) b. 6( vec bxx vec c) c. 3( vec cxx vec a) d. vec0

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 a. 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

Value of [ vec axx vec b vec axx vec c vec d] is always equal to ( vec a . vec d)[ vec a vec b vec c] b. ( vec a . vec c)[ vec a vec b vec d] c. ( vec a . vec b)[ vec a vec b vec d] d. none of these

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

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

Let vec r be a unit vector satisfying vec rxx vec a= vec b ,w h e r e| vec a|=3a n d| vec b|=2. Then vec r=2/3( vec a+ vec axx vec b) b. vec r=1/3( vec a+ vec axx vec b c. vec r=2/3( vec a- vec axx vec b d. vec r=1/3(- vec a+ vec axx vec b

If vec aa n d vec b are two vectors, then prove that ( vec axx vec b)^2=| vec adot vec a vec adot vec b vec bdot vec a vec bdot vec b| .

Let vec aa n d vec b be two non-zero perpendicular vectors. A vecrtor vec r satisfying the equation vec rxx vec b= vec a can be vec b-( vec axx vec b)/(| vec b|^2) b. 2 vec b-( vec axx vec b)/(| vec b|^2) c. | vec a| vec b-( vec axx vec b)/(| vec b|^2) d. | vec b| vec b-( vec axx vec b)/(| vec b|^2)

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