Let ` vec aa n d vec b` be unit vectors that are perpendicular to each other. Then `[ vec a+( vec axx vec b) vec b+( vec axx vec b) vec axx vec b]` will always be equal to `1` b. `0` c. `-1` d. none of these

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

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 vec a , a n d vec b are unit vectors , then find the greatest value of | vec a+ vec b|+| vec a- vec b|dot

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

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.

If vec a+ vec b+ vec c = vec 0 then prove that vec axx vec b= vec bxx vec c = vec cxxvec a .

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 and vec b are two vectors, then prove that ( vec axx vec b)^2=|[vec a.vec a,vec a.vec b],[vec b.vec a,vec b.vec b]| .

If vec a and vec b be two non-collinear unit vector such that vec axx( vec axx vec b)=1/2 vec b , then find the angle between vec a and vec b .

Prove that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b) and interpret it geometrically.