If ` vec aa n d vec b` are two given vectors and `k` is any scalar, then find the vector ` vec r` satisfying ` vec rxx vec a+k vec r= vec bdot`

If vec aa n d vec b are two vectors of magnitude 1 inclined at 120^0 , then find the angle between vec ba n d vec b- vec adot

If vec a and vec b are two vectors such that | vec axx vec b|=2, then find the value of [ vec a vec b vec axx vec b].

If vec c is a given non-zero scalar, and vec Aa n d vec B are given non-zero vector such that vec A_|_B , then find vector vec X which satisfies the equation vec A . vec X =c and vec Axx vec X= vec Bdot

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 An d vec B are two vectors and k any scalar quantity greater than zero, then prove that | vec A+ vec B|^2lt=(1+k)| vec A|^2+(1+1/k)| vec B|^2dot

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

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| .

vec aa n d vec b are two non-collinear unit vector, and vec u= vec a-( vec adot vec b) vec ba n d vec v= vec axx vec bdot Then | vec v| is | vec u| b. | vec u|+| vec udot vec b| c. | vec u|+| vec udot vec a| d. none of these

If vec a and vec b be two unit vectors such that vec a+ vec b is also a unit vector, then find the angle between vec a and vec b

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