If ` vec aa n d vec b` are two unit vectors incline at angle `pi//3` , then `{ vec axx( vec b+ vec axx vec b)}dot vec b` is equal to a.`(-3)/4` b. `1/4` c. `3/4` d. `1/2`

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

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 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

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

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 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 a. 1 b. 0 c. -1 d. none of these

If vec ba n d vec c are two-noncollinear vectors such that vec a||( vec bxx vec c), then prove that ( vec axx vec b) . ( vec axx vec c) is equal to | vec a|^2( vec bdot vec c)dot

If the angel between unit vectors vec aa n d vec b60^0 , then find the value of | vec a- vec b|dot

Let vec a* vec b=0,w h e r e vec aa n d vec b are unit vectors and the unit vector vec c is inclined at an angle theta to both vec aa n d vec bdot If vec c=m vec a+n vec b+p( vec axx vec b),(m ,n , p in R), then a. -pi/4lt=thetalt=pi/4 b. pi/4lt=thetalt=(3pi)/4 c. 0lt=thetalt=pi/4 d. 0lt=thetalt=(3pi)/4

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